Is This Common For a Custom-Built Torque Converter???

The converter consists of much more than what you see outside. The weight includes everything within the converter, too. That is a small amount of weight to get one neutral balanced, everything considered. Look how thin those little weights are. There are normally two weights on a 360 converter about 1.25" long and roughly 1/4" or more thick. That is a lot of weight. Enough weight for an externally balanced engine, not what you see here. Just because it has weights (and a small amount, IMO) doesn't make it a bad thing. I certainly wouldn't condemn it for that alone. The next one you get may have weights as well. That simply means the converter WAS balanced.
Imagine if you put your driveline all together as new and the car or engine had some kind of objectionable vibration.
The first thing you would be looking for is to see if everything has been balanced lol. I,m not saying that a driveshaft or converter cannot be balanced without any weights on it, but if there were none and you have a problem you would be questioning whether the builder forgot to do it. At least if you see some weights on there you know it was done. I think this guy bought another converter for no reason, imho. The bolt holes will probably line up if clocked at the right position as well. IMHO.