I am not a specialist of the R8, but the way it felt at SCI was that, truly, as
Red Leg said, most of the weight is in the barrel. I asked the rep. to put a sporter barrel on that specific receiver to verify it, and it was night and day. They did not have a scale on the booth to measure the exact weight...
I agree with
Philip Glass that as a .375 H&H the one at SCI was a bit heavy. But it would be about right in .458 Lott. Sorry for having confused the issue: I should have specified that THIS specific rifle was in .375 but that I was thinking .458 Lott (same barrel contour hence ever slightly lower weight due to larger bore) in answer to your question. My bad.
I have since checked on the web site
https://www.eurooptic.com/blaser-r8-professional-big-bore-stock-receiver-savanna.aspx but they do not list the weight of the stock/receiver only... I have an email into them with that specific question as well as the specific weight of a couple different specific barrels.
My thinking at this stage, if I do it, would be to get the "professional big bore" steel receiver, and to mount on it various barrels of various contours and various weights adapted to my notion of what they should be for various calibers. They are all cross compatible. The only thing is that a standard sporter weight barrel will seem floated very generously in the receiver/stock channel designed for the heavy contour barrel. It is noticeable when you look for it, but not offensive. Beside, it will favor faster cooling with increased air flow.