It's just an almost imperceptible shift of emphasis. In the first instance, the lyricist is saying...
1: I've given [up] something for you [for your benefit]...
...where in the second instance it's more a case of asking for something in return...
2: ...so you should give something to me.
In both cases, the "underlying" emphasis is on the situation from the speakers's point of view (in #1 he does something for someone else, in #2 he wants them to give something to him in return).
As J.R. comments, the difference is negligible, and the two prepositions could feasibly even be reversed.
Note that in general you give [something] to someone. But in this particular case the meaning is closer to give up (sacrifice, go without). This can be seen as a "self-contained action" rather than the giving of a "thing, object". In such contexts, for is used to specify who benefits from the action.
My wife is asthmatic, so I gave up smoking for her [optionally: sake, benefit, comfort, health, etc.].
✲My wife is asthmatic, so I gave up smoking to her. (where ✲ marks a usage as unacceptable).