Load cell weight distribution on rectangular shape instead of square
Newton's second law says that if a force acts on a mass, that mass will accelerate at a rate proportional to the force and inversely proportional to the mass.
All that means for your scale is that if you are not being accelerated up or down, the net vertical force on your body must be 0. Since your body has weight, and the net vertical force on your body is 0 (you aren't accelerating, are you? :) then the downward force must be balanced by an exactly equal upward force. That upward force is the sum of the upward forces exerted by each load cell. Their contributions may individually change depending on where you stand, but their sum must exactly equal your weight.
Note that we have said nothing about the placement of the cells! If your platform allows it, you could move one of the cells 6 (or 60 or 600) feet away from the the others, for instance. The total upward force must still be the same.
So the bottom line is:
F_lc1 + F_lc2 + F_lc3 + F_lc4 == your weight
no matter where you place the cells.