Think of it this way… When the strings are tuned to pitch, they're balancing the pull of the tremolo springs, so everything is at equilibrium.
If you bend a string, which increases its tension, it is going to pull harder on the bridge and transfer that tension to the other strings so they're going to go out of pitch an equivalent amount lower. The higher strings are under more tension, so they'll go out of pitch further than the lower strings, but all the other strings have to change pitch because of the tension change, it's just physics because of that "for every action there's an opposite but equal reaction." thing. And, as you push the string you're bending and the others are reacting, it's going to take more pressure from your fingers to move the string farther to balance the springs and other strings.
You can easily prove this to yourself by bending one string and watching the bridge, then bending two as you watch it. Bend the B string without playing it while holding the E and then play the E and you'll hear it be flat. Then compare the same things to a guitar with a fixed tailpiece. A fixed tailpiece doesn't transfer the tension to the other strings, so bending doesn't affect other strings and the bend is always the same distance for that particular string.