Digital Scale (461)

We have some apples, bananas, and cherries. The weight of each piece of fruit is a positive integer. All pieces of fruit of the same type weigh the same. We have weighed some combinations of fruit on a scale with a digital display. The scale always shows the exact weight, but its display is faulty: some segments that should be on remain off. In each puzzle, the faults are consistent between weighings. Determine the weight of each fruit type.

Reference: WPC 2016 (65)