If I understand you correctly, you're looking for the following equation:
The overall "weight" of a dice with N sides is (N/2)*(n+1).
1 The total "weight" for 6 sides is (6/2)*(6+1) = 3*7 = 21.
The calculation is then straightforward.
1 -> 6 / 21 = 0.28571428571
2 -> 5 / 21 = 0.23809523809
3 -> 4 / 21 = 0.19047619047
4 -> 3 / 21 = 0.14285714285
5 -> 2 / 21 = 0.09523809523
6 -> 1 / 21 = 0.04761904761
6/21 is obviously 6 times the size of 1/21, therefore that part is correct. Finally, here's the bottom line:
0.28571428571 6/21
+ 0.23809523809 +5/21
+ 0.19047619047 +4/21
+ 0.14285714285 +3/21
+ 0.09523809523 +2/21
+ 0.04761904761 +1/21
--------------- -----
0.99999999996 21/21
In any case, the left side is close to 100 percent. Being what it is, rounding is inevitable. The right side demonstrates that this is a rounding issue rather than an error.
*This equation (and its variation (N/2)*(N-1)) are quite useful. It's a shortened version of 1+2+3+4+5+6...