As you see in my sig I have a squier strat. Although it's only really a squier neck now, because all the rest of it has been replaced with better parts. My original squier bridge sucked, and the tremelo would take it out of tune immediately. When I got a new bridge, it did the same thing. Is there any way to make the tremelo work better without getting a floyd rose? Adding extra springs? Locking tuners?
Schaller locking tuners m6 minis, adjust the spring tension, make sure your springs are in good working order, graph-tech nut, put some graphite on the saddles. Adding extra springs is not the solution as the tremolo will be too difficult to use. Do this and you should be ready to rock n' roll, don't get a "Fraud Rose" because I said so I won't go into the reason's why they suck so much right now though.