on (one's) side
Supportive or in aid of one or one's idea, plan, intention, etc. We're all on your side, Jerry. We just want to see this issue resolved as quickly and easily as possible. If she's going to win this case, she'll need one heck of a legal team on her side.
on your side
If something is on your side, it gives you an advantage and helps you to achieve something. We at least have time on our side. There really is no hurry. I have been very lucky this year. Luck seems to be on my side.