String Bending with a floating tremolo - help

[Natima]

Every time I bend a string the bridge dips in and whacks the other strings out of tune so I cant use double bends, it also means I gotta bend more.

Any way of fixing this? I have more springs that came with my strat, but I would like to keep the bridge floating.

 

[Natima]

I had 3 springs, but I've added the other two now. seems a lot better but its a bit too stiff now. I think ill have to look into different spring sizes/configurations.