When to re-balance a motor?

I think I may have overestimated the ring set weight when I ordered my custom billet crankshaft for a small block Mopar. I weighed a used set of rings I had on hand for a 340 with stock pistons and 5/64" top rings and they came out to about 57 grams.

However, come to find out the NOS TRW pistons I have to install (L2322F) use smaller 1/16" top rings, which I assume are going to weigh less. Anyone know the difference in weight between the two ring sets? And how much of a weight difference can I get away with? (will be mostly a street motor with yearly drag runs just for fun). I am willing to re-balance the rotating assembly, but would rather not ($). Thank you.

ring set.jpg