As Rick C said earlier in this thread: Be patient. Changing gauges on a trem bridge throws off the entire ecosystem of your trem. Especially if you want some float. In my non professional experience this is the checklist you need to use, and some things need to be checked off more than once and in changing order, and you'll need to tune at and in between every step:
-Change strings (duh)
-adjust spring tension to the trem
-examine action and change saddle height. Don't get too overzealous here, don't try to get it perfect in one go, it will keep adjusting.
-adjust intonation on the saddles
When you change the spring tension, it will change the action. When you adjust the saddles, they will throw off the spring tension. When you tune, it can change both of those. Usually I will go back and forth between those two steps until I am satisfied, always always tune every time you finish one of those adjustments.
Move on to saddle intonation after that point, and if you're getting buzz at the lower frets adjust the truss rod slightly. Every movement of one piece of hardware affects all of the others. Once you do that it will change all the other stuff you worked on all over again.
Patience, grasshopper.