Hi, yes I was definitely being serious if the trailer is bouncing then the axle is basically acting like a solid axle (if it is the axle which I would agree that it sounds like). I know there is a % of weight you are supposed to rate the axle at as compared to the weight of the trailer but I don't recall but it's up there, not 60%, you probably already know this but all that mumbo jumbo is moot your axle is already bought and paid for. I like your idea about weights since they are easier to move.
Before adding weights, you might also check your tongue weight and add more weight to the tongue if it is too light. 10-15% of the total weight should be there.
People always say you don't need to balance trailer tires "because people don't ride back there", but their answer actually supports the reason to balance because your stuff does and since it is getting bounced all over the place, balancing the tires may help. People think I am nuts but I tell them to do it anyway and get out of my face!
Don't get me started on passenger tires, people will string me up a tree.