*If the lowest card cost in coins is zero, use a weighted arithmetic average, where the weights are the weights of the players owning that respective card, in Newtons.
The good news is that for arithmetic weighted averages, the actual unit of weight measurement cancels out and doesn't matter.
Unless I don't understand that clause, if I weight 100 kg and I am playing against my (hypothetical) 50 kg girlfriend, the weights do matter.
Well, first of all, 100 kg is your mass, not your weight.
His point is that if you measure the weight in a different unit, it will cancel out of the weighted average:
X = sum(w_i x_i , i=1..n) / sum(w_i, i=1..n).
Changing units is just changing the weights by a constant factor, which factors out of the numerator and denominator.