Well, that could be a big factor! Try taking the bottom plate off and checking the bronze bushings. They have a flat that has to be facing the bottom plate or things could be out of plumb. That could cause the rocking and also be a major issue as far as traction.
With the extra weight, the BEEP shouldn't have any issue pulling a dozen cars on flat track as long as they're free-rolling with needlepoint axles.
Even the Menard's boxcars, pretty notorious for the high rolling resistance, I can pull six of those with the stock BEEP. It's working a bit harder for these six Menard's cars, but no real sweat.