Is there a method for calculating change in V-speeds with a change in weight for a Cessna 172?
Instead of doing detailed calculations like you were in a jet, there is a useful rule of thumb advocated by author/instructor William Kurshner for working that out, which while not exact down to a fraction of a knot, is conservative and easy to do and is therefore perfect for regular GA flying.  

Reduce Vs/Vr by half of the percentage of the weight reduction.  So if stall speed is 50kt at gross, and the weight reduction from 2297 to 1807lb is about 21%, and half of that we can round up to about 11%, your stall speed is going to be about 45 kt at that weight.

So if I was using say, 55kt as a rotation speed at gross (I seem to remember that's what it was on the 172), I'd use about 49 kt at 1807 lb.  Close enough for 99.9999999999% of normal operation in a Chevy Biscayne Of The Air like the 172.