Went through the same process a couple months back. Went with a Z3 3-10x42 on my Finnlight 6.5 Swede. Put a 2-12 Vx6 on it later to try and couldn't tell a difference in the time it took to swap them. I had the same issue comparing the 2 scopes. Unless i had them side by side, I couldn't see a difference in glass. Literally had to peep through each within a second of each other to notice a difference.

Like my Finnlight, I wouldnt say your Weatherby is a true ultralight and thus the weight of the scope within reason wont likely matter. I dint notice any "balance" issues. Perhaps maybe with my NF 5-22 but not any hunting scopes ive tried.