Italian game 3...h6

I notice that when the game goes

1 e4 e5 2 Nf3 Nc6 3 Bc4 
black offen continues with h6
I can understand this move because it prevents Ng5 but I'm always confused by such a move because I'm not sure if this is actually a good move.

First of all, why would I do Ng5? Yes, I then could do Nf7, double attack on queen and rook but that also means moving my knight 3 times which is a bad thing in the opening.

It also weakens the deffense of the king in case black castles on the kingside.

So, because of this reasoning I am wondering if there is a deeper thought behind h6 that I must be missing 

Reason for asking is that I see this response from black quite often. 

The response is based on two things: Lolli attack which indeed starts with Ng5 but also on preventing the dark square bishop of white coming to g5 and pin any future Knights on f6, so it removes the g5 square from two pieces of white. Off course h6 isnt very active, I myself don't 'like h6 but thats maybe my play, white will be up in development more because h6 doesnt help black with his piece development.

Moving the knight multiple times isn't bad because it allows tactics, stops black from castling maybe and winning the f7 pawn is a decent compensation.

SO it's not as bad as I think and the defensive advantage can justify the loss in development?

I think it's a poor move and a waste of time. Not terrible or losing or anything but not principled.

Play d4 and open the centre with a development advantage.

Thanks.

And then probably

4 d4 exd4 5 Nxd4 Nxd4 6Qxd4

Is this a good line? By the end I'm up on development. 

I don't think black should play 5...Nxd4 because it just helps white's development advantage.

Bc5 for example should be better.

Thanks a lot for this explenation! Those lines really make a lot of sense! 

I also now know how to respond to an h6... 
Coincidence or not but I am playing a 1600+ player who did a 3 ... h6 on the italian game :)
Perfect time to practice my new knowledge 

It does not look particularly inspiring if white replies with 4.d4!, when ...h6 is more or less a move wasted for no good reason.

Actually it's quite playable one move later- I have played so myself as Black several times, and have a pretty good score:

Black will play ...g6 and set up a Pirc-like position, where white has commited himself to the "passive" d2-d3 instead of d2-d4. Of course this allows the Lolli (4.Ng5), but I never had any serious issues with that as Black.

The plan for Black is the usual one: He reacts according to the way white treats the position, there is no generic formula. Both mid term plans of ...f5 and ...d5 are on the cards. This system (some name it the Beliavsky variation) is still well respected at top level. This system is not my idea, of course! 

I have not kept record of all my games in the variation (there are more than one dozen), but at least one of them is included in the chess.com database.

http://www.chess.com/games/view?id=542530#

3..h6 is  obviously bad, as it loses a tempo. White right away gets the better game after 4.d4!

So which one is better for black. ..?

Since I played 3.Be7 ...people mostly play 4.d4

3...Bc5, or 3...Nf6.

Both are equally good, it's just a matter of taste (and playing style).

I have played 3...Nf6 a lifetime, but 3...Bc5 is not worse, by any means.

Nf6 leads to 2 knight defense. ..I like to play slow game then more attacking game

3..h6 is the main line for the Italian Game in blitz 1100-1300 Aloha!

3...Nf6 is my preferred move because I also play Nf6 against the Scotch and any other random sidelines.  Plus its fun beating Ng5ers 

3. ... Nf6. Just like Fixing_A_Hole, I salivate when I see 4. Ng5. 

A bad third move 3...h6, it can only help white increase his development..

3...h6 is a reactive move.  Black is preparing for something that hasnt been played yet.  Beginners love moves like this, simply because it prevents Ng5.  Be proactive, not reactive.

Meh, playing 5...Nxd5 is garbage.