A possible solution...?
Let Total Weight(X) = Number of Sides(A) x Weight of Armor(B) + Total Number of Weapons(C) x Total Weight of weapons(D)
All of which are constants.
Moreover, in simplicity: X = AB + CD, but this would only refer to the bot when not in battle. Of course, this value would change when under damage variables.
So If X is not = F(After battle)
Then X would be equal to X(Total weight) / Total Hitpoints of Damage dealt to Weapons for F (H of F) x Total Hitpoints of Weapons (W)/ Total Hitpoints of Weapons (W). Or in other words, F = X/ (H of F x W) / W.
Due to the fact that after the battle is over, the bot may lose parts, and in turn, lose weight.