Sounds like an inexpensive, and perhaps poorly manufactured, rim to me. The welds should not present that much of a problem. Yes, sometimes the spoke tension on either side of the weld is slightly different from the rest of the wheel.
Are you using some measuring device to check tension? It could be that you have large differences in spoke tension throughout the wheel and that's causing your problem.
I can't imagine breaking a spoke just by applying tension to it. They have to be WAY too tight or they are damaged spokes to begin with.