I am not a medical professional, but my understanding is that the issue with birth control is increased risk of blood clots. Heart/cardiovascular disease run in my family, for that reason, I am at especially increased risk of complications. Generally speaking, I would suggest that you trust your doctor unless you have a reason not to. Like, if you noticed you felt unwell on BC all the time or if, like me, you start having strange GI distress all the time and the doctor says "no, it couldn't possibly be BC".. but I sort of suspected it was so I took myself off the pills and voila! No more weird GI issues. ... in situations like that, I would say take the matter into your own hands. But it sounds like you have a pretty good reason to keep taking it (i.e. cysts on your uterus).

If I were in your position, I think I would keep working on the lifestyle piece and once I was feeling more confident in that, then I might take another look at stopping the BC.

You could also just talk to your doctor about your concerns. Be blunt, say Hey, I heard these things and I'm concerned, can you tell me why I'm better off staying on the birth control?