Welcome Ligeia! I have never heard of consuming lots of timothy hay as being a bad thing. It is wonderful for their digestive system, good for their teeth, and very low in calorie. So it is almost impossible for hay to cause weight gain.
In fact, some bunnies who have extremely sensitive digestive systems end up having hay as the main part of their diet.
I am happy to hear that your bunny loves hay and eats "tons" of it. It will keep her digestive tract healthy which is one of the most important parts of a rabbit's health. And actually, many bunnies don't eat enough which can lead to a whole host of problems. Gi stasis, poopybutt, teeth issues, etc.
To make sure she is getting a healthy balance of vitamins though, does she eat her greens and pellets?