I have had a Mauser .375 that went about 6.5 pounds plus scope. I couldn't keep a scope zeroed on that rifle. I lost count of how many Leupolds that rifle ate, including an older M8 4x that I bought in like new condition. After a few years and 600-800 rounds, I decided that rifle was a little light.
Have had a Kimber Talkeetna, which was just about right regarding weight for a .375. Also, currently have a Model 70 Classic Stainless and Blaser R8, which are both plus or minus 8 pounds before scope and seem about right.
IMO, around 8#'s all up is about ideal for a .375 H&H.
I don't want or need a 7# big boomer.
DF
