I would like to make the increments for zooming using the middle scroll wheel smaller. Right now when I get somewhat close to my object, in both Edit and Object Mode, just one more increment on the scroll wheel and I have zoomed in way too far.
Is there a way to change this increment distance or amount?
You could try switching to Orthographic mode with Numpad 5. Or for finer zooming instead of rolling the scroll wheel, hold Ctrl and instead hold in the scroll wheel like a button and move your mouse up and down.