Searching for Mean(ing)

We can make all the whole number averages in between 3 kg and 8 kg, using combinations of those two weights:
3 kg weights 8 kg weights Average
1 4 7
2 3 6
3 2 5
4 1 4

We can make all the whole number averages in between 2 kg and 7 kg, using combinations of those two weights:

2 kg weights 7 kg weights Average
1 4 6
2 3 5
3 2 4
4 1 3
We can make all the whole number averages in between 3 kg and 10 kg, using combinations of those two weights:

3 kg weights 10 kg weights Average
1 6 9
2 5 8
3 4 7
4 3 6
5 2 5
6 1 4

In each case, the total number of weights required is equal to the difference between the values of the two weights.

So, if we have 17 kg and 57 kg weights, we can make whole number averages with 40 weights:

17 kg weights 57 kg weights Average
36 4 21
13 27 44
5 35 52

We can also make non-whole number averages:
3 kg weights 8 kg weights Averages
1 9 7.5
3 7 6.5
5 5 5.5
7 3 4.5
9 1 3.5

and other decimal averages:

3 kg weights 8 kg weights Averages
1 49 7.9
2 48 7.8
3 47 7.7