Rotating assy balance

When I pulled the engine apart I stamped each rod and cap.
I am so on a budget here, New rods? They said the pistons would be destroyed if had to be changed. He did weld up the crank some and add a hole. When I put #8 cap on #5 rod it binds before it seats. I don't like it.
I thought the whole purpose of balancing was to get all the components to weigh the same before you made bob weights to balance the crank. This looks like it would shake apart and kill every bearing on cam break-in. But i'm naive. Still 13 grams between #3 journal and #4.
I guess I'm headed back to the machinist for some explanation, but, in my opinion, this is not right.DSC01045.JPG DSC01046.JPG DSC01047.JPG