Okay, so the approach of welding the sides to the ends didn’t work so well. The weights themselves pose a much larger gluing surface, however, and so, I made them integral to the cars.
To do this, I first coloured up some paper to look like the bottoms of the deck boards, and spray-glued it to the bottoms of the weights. I actually glued this to the wooden parts of the side sills with white glue, before adding epoxy between the plastic part of the side sills and the weights. To ensure the two 1/32″ thick weights fit beneath the decks, I clamped them to set.
To tell the truth, the plastic side and end sills seemed like a good idea at the time, but they’re turning out to be more trouble than they’re worth. Being only .020″, they’re too thin to hold a straight line without the wood backs. The result is that holding these cars square and true is more challenging that it should be.