The elo calculation for wins and loses depends on the elo of your opponent. For people within 20-30 elo you should get +7 for a win and -7 for a loss. If you are above 30 elo it might be +7 for a win, -1 for a draw and -9 for a loss. If you are above 100 elo it might be +3 for a win -8 for a draw and -20 for a loss. Lastly your first few games of a time control are going to be 5x-10x the amount of normal elo changes to attempt to place you at the right elo as quickly as possible.
Big difference in my Elo rating when it drops, vs. when it increases

It seems like whenever I lose a game, my Elo will drop by sometimes as much as 70 points in a single game, yet when I win, it only goes up by a small handful of points, so my question is, why does a loss make your Elo rating change by such a larger margin than a win?
This is because of how the rating system stabilizes your rating. As you play more games and your rating become more accurate then you'll gain roughly the same amount of points as a loss would have you lose.
It seems like whenever I lose a game, my Elo will drop by sometimes as much as 70 points in a single game, yet when I win, it only goes up by a small handful of points, so my question is, why does a loss make your Elo rating change by such a larger margin than a win?