in deference to paul's correct observation, the balance of your tremolo system needs to be adjusted so that the at rest position is more towards the body...
if you've changed gauges of string, this is what will happen with a floyd rose. you'll need to spend some time re-adjusting things. tighten the screws in the back cavity of the guitar a little (start with more aggressive changes, fine tune until it's even), and re-tune the guitar to pitch, check the bridge height, and repeat until it is level with the body below it.
as violation said, you will want to check that the knife edges are seated correctly on the posts, so that they move freely, and if you're way out (as you are), adding a spring might be the first move *edit* if this has "just happened", you might find that one of the springs has slipped out or broken, which would make an easy fix).
if you haven't done any of this before, you might want to get someone to show you the process, or take it to a repair tech for adjustment. good luck
like evreyone says ,your string tension is greater then you spring tension,
once you get it tune up and set up correctly,
tip number 1 with a floating bridge,so you dont have this problem again
change 1 string at a time,pull the old one off,put the new one on ,tune it
to as close as possible,doesn't have to be exact,you can hear it as you tune up,then move to the next string,then tune them all then stretch them,repeat that process 3 or 4 more times and you should be good to go
use a block of wood. Lift the trem arm up so your bridge is level with the guitar body. Push a block of tapered wood between the trem block and body. This will lock the trem. Now tune to pitch. Once tuned tighten the trem screws until the block of wood falls out. Voila, you are done and you dont have to fight the trem, while you do it.
To make you block simply taper a small peice of wood from half inch to one inch. That little block will be a handy tool forever.
I don't have feeler gauges, so I use guitar picks stacked together to approximate the correct spacing between the body and the rear of the trem. I also use a 1.5mm pick and a 2mm pick to adjust string height at the 12th fret.
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