If we accept that the power required curve is representative of the fuel flow curve then we can use it to test how fuel flow will vary with weight. But we can also test the effects of speed.
If we increase weight, the power required curve moves up and to the right, but it remains nested within the previous (lower weight) curve. This means that for a given weight increase, the % fuel flow penalty is less at higher speeds.
Using one of the charts in the CAP 697 Flight Planning Manual (for the JAR exams) I have found that (in the climb) a 5% increase in weight causes a 16% increase in fuel flow. But the scale of the chart is very small so the figures are obviously very sketchy. But all of the cruise charts are for a single aircraft weight, so they are of no help.