Moving from light gauge strings to heavier gauge stings on a Floyd Rose style bridge will cause you problems; unless you take care to set the bridge up properly, or have a shop or someone set it up for you.
As Tim said in his answer, once the guitar is set up properly, there should not be much of a difference, in terms of action at least. The string tension will certainly be greater. Floyd Rose style bridges usually use 3-5 springs (though I have seen one with two springs and .009 gauge strings) to tension the strings to the proper level. If you are doing this change yourself, you will probably want to take a look at the bridge cavity on the back of the guitar.
You should find a claw apparatus that is affixed to the guitar body with wood screws. If that claw is already close to the body, then you don't have much room to apply extra tension the springs, and you may need to get an extra spring or two in there to make up for the difference. Pulling the old strings off, and then finding you can't tension the bridge properly due to a lack of springs is not a fun time.
Getting the springs/strings set up is a careful balancing game, and it is usually a lot of back and forth to get it all dialed in right. You will want to undo the locking plates at the nut so you can restring and start to tune the guitar, and watch what happens to the bridge as you start to tune the strings to the desired pitches. Keep an eye on the bridge, and if the back of the bridge starts to raise up past where it used to be, you will want to back off on the tension of the strings, and tighten the screws attached to that claw. Go back to the strings and tune up. A bit of back and forth like that is always required when setting up a Floyd Rose bridge with strings of a different tension. I own two guitars with Floyd Rose bridges, and I've been through that dance more times than I can remember.
When you get the springs/strings set up to the right tension, try to handle any intonation changes afterward. You will also want to pay attention to the neck, in case the truss rod needs any adjustment to put the action back to where you expect it to be. Moving up to a heavier gauge of strings may call for tightening the truss rod a little bit, which you always want to be careful with. Replacing a broken truss rod is not trivial.
The thing I really like about a Floyd Rose bridge is that once it's all dialed in and locked in place, they tend to be rock-solid. I can pick one up after a half year of it sitting there, and it's still be properly in tune. Worth the effort!