As Ted's suggestion is such a cheap and easy one to undertake, I'd say it's certainly worth a try.
As for the barrel weight, I have no experience of the latest guns with the barrel weight. Mine is an earlier barrel weight one. But I'd doubt whether that would be the cause.
Give it a try with the resting method I suggested earlier, please.
If you did think it's a balance issue, you could try adding some weight at the rear of the gun temporarily to see how that alters things. A heavier scope is sometimes all that is needed. Or you could try strapping something heavy to the butt end (as I say, just a temporary thing to see if it changes things).
In your opinion, does the firing cycle feel harsh to you?