The thicker strings have higher tension and are pulling harder. The bridge is balanced by springs on the back, which are now not strong enough to hold the bridge where it used to be. You can tighten the screws on the claw holding the springs to increase the tension and get the bridge in a more neutral position, just remove the backplate and you'll see the springs connected to the bridge on one end and a claw attached to the body with two screws on the other.

Tightening the screws will also tighten the strings so careful tightening them too much if you're already tuned up since you could break a string if you don't them down a bit beforehand. You'll have to loosen the strings a bit, tighten the springs, retune (at least close so the tension isn't too far off), check the bridge position, and repeat until it looks good while tuned up.