Could be bad connection.
I see my opponent connecting and reconnecting every move? Are they cheating?

It could just mean that they are having internet difficulties or trying to watch YouTube while playing chess at the same time or they could be going back and forth between the board and an engine. I highly doubt at your level any one is sophisticated enough to know how to use an engine's suggestions during a game so it's probably one of the first two.
Copied and pasted from the "Cheating Forum" group:
If you suspect someone to be cheating, please use the "Help & Support" link at the bottom of the page. When that page opens, click on the upper right side where it says "Contact", select "Report Abuse" from the menu on the upper left, and submit a ticket. A direct URL to the contact page is: https://support.chess.com/customer/portal/emails/new. Also see http://www.chess.com/forum/view/community/chesscom-policy-on-cheating. Please respect the group rules and each other.

This was a 10 min blitz game so I found it wierd that literally every single move the person would disconnect and then reconnect to make a move. What else can you possibly be doing every single move?

It is probably not cheating. One of the advertised benefits of paying for a membership on this site is fewer disconnections. I know that my connection is usually more stable than it was before I paid up.
Having that stability of connection problem is a real disadvantage when you are playing. Taking 2 or 3 minutes out of a 10 minute game really shifts the odds.

This was a 10 min blitz game so I found it wierd that literally every single move the person would disconnect and then reconnect to make a move. What else can you possibly be doing every single move?

It is probably not cheating. One of the advertised benefits of paying for a membership on this site is fewer disconnections. I know that my connection is usually more stable than it was before I paid up.
Having that stability of connection problem is a real disadvantage when you are playing. Taking 2 or 3 minutes out of a 10 minute game really shifts the odds.

Before I started paying I got regular messages from chess.com inviting me to pay up. I am pretty sure that one of the advantages that was mentioned was less disconnections. Experience tells me that that is the case.
It was also annoying to have flashing advertising going on beside the gameboard, and once you pay, that disappears.

I've said it before and I'll say it again...
I've played games wherein I'm winning, more time on the clock than my opponnet, they disconnect/reconnect and the times have changed. I read on one of the forums that if you click regfresh the page it stops the clock for you for a few seconds. I don't know.
But I see it all the time and many times it's followed by outrageously good playing.
And those of you who think cheating only occurs in highly rated segments...non-sense. Someone above made comment that lower rated players won't know how to use an engine. I challenge you to play 2 minute bullet chess players like "grandmastered" who's rated between 450 and 750ish on any given day. The guy is WAY better than that. Some people just don't care and give away points. There are many sharks down under the surf.
Turning on an engine does not affect the internet connection you silly people.
Lots of disconnects can be tried to scam the clocks, but AFAIK that doesn't work on modern websites.
I've had games where I'm the one reconnecting every move... it's because I'm using a wireless hot spot and it seems the ISP likes to throttle the hell out of anything you try to do.

Most likely causes of disconnections are other processes running on the computer. Flash is one that can cause connection issues and should be disabled for the site (it isn't needed for Live).
Discussions about cheating are not allowed in the general forum so please don't discuss that here.

@binary dude: i don't see that anybody above said chess engines are casusing the reconnects. I re-read because you said that. You wasted my time by referencing something that has nothing to do with what people have said so far in this thread. I don't get it.
@the constant "poast cheating here" comments I as sick of seeing that as you are of seeing cheating posts in the genreal forum. Chess.com does not offer a cheating forum when you click on the forums tab. It doesn't even mention what you should do with those complaints - a natural place to put that information I would think. So until that is done you should stop clicking on these forums and go do things you like to do.
As for if cheating discussions belong in the "general" chess forum. Yes. It's a general topic with respect to chess. And how you say that ANY chess related topic doesn't belong in a forum called "general"??? Give me break. It's slicing and dicing comments why to much.
@binary dude: i don't see that anybody above said chess engines are casusing the reconnects. I re-read because you said that. You wasted my time by referencing something that has nothing to do with what people have said so far in this thread. I don't get it.
@the constant "poast cheating here" comments I as sick of seeing that as you are of seeing cheating posts in the genreal forum. Chess.com does not offer a cheating forum when you click on the forums tab. It doesn't even mention what you should do with those complaints - a natural place to put that information I would think. So until that is done you should stop clicking on these forums and go do things you like to do.
As for if cheating discussions belong in the "general" chess forum. Yes. It's a general topic with respect to chess. And how you say that ANY chess related topic doesn't belong in a forum called "general"??? Give me break. It's slicing and dicing comments why to much.
Guy above me:
"I see it all the time and many times it's followed by outrageously good playing. "
And OP implies it:
"What else can you possibly be doing every single move?"
And chess.com's policy is due to wanting to keep cheating visibility low. The less the general population is aware if it, the more business they can do. At least I assume this is their reasoning.

OK I can see how you thought that's what I meant but it wasn't.
What I think is that they are logging off, then on, or pressing the refresh button, and while the browser is sending and resending data (and does the clock change??? some people here say it can) they study their engine and then make a move.
Listen I don't have a clue about hacking, cheating, technical limitations of engines, browsers,etc. But I'm convinced it's possible and happens.
I swear on the life of my dog (she's 13 and will dead soon anyway) that I played a game in which my opponnent pick up more than 45 seconds of time after long disconnect on their end. This has happend MULTIPLE times. Not hundreds or even dozens. Just a few. But it's creepy. That's why it bugs me.

...
@the constant "poast cheating here" comments I as sick of seeing that as you are of seeing cheating posts in the genreal forum. Chess.com does not offer a cheating forum when you click on the forums tab. It doesn't even mention what you should do with those complaints - a natural place to put that information I would think. So until that is done you should stop clicking on these forums and go do things you like to do.
As for if cheating discussions belong in the "general" chess forum. Yes. It's a general topic with respect to chess. And how you say that ANY chess related topic doesn't belong in a forum called "general"??? Give me break. It's slicing and dicing comments why to much.
That discussion is against the posting rules for the forums.
https://support.chess.com/customer/en/portal/articles/1444879-fair-play-on-chess-com-what-you-need-to-know
Thst explains what you need to know
If you want to have the discussion, there is a group with its own forum for that.
https://www.chess.com/groups/home/cheating-forum
What does it mean when you see an opponent connect and reconnect for every move?