I've had a bunch of A-series Sakos over the years, including two AV's in .375H&H. I've also owned a couple of 75's and 85's since then. IMHO the A-series was the pinnacle of Sako quality, which seems to have dropped with each new model brought out since. Not sure about the latest S20's et al, haven't even handled or seen one.
I never weighed a rifle back then, but mine (they were all wearing the Hunter style stock) felt very well balanced and not at all heavy. Beautiful wood and metal fit and finish. Accuracy of every Sako I've ever owned was excellent with any decent ammo; I don't think I ever saw a group open up to 2MOA and most were half that or better. I had an AI in .222, with the pencil barrel, that printed sub-0.5MOA groups if you took your time and kept it cool. My second .375 did the same with some ammo...and a half-inch group looks much more impressive when each hole is .375-inch.
Weak points? The original recoil pad on several of mine grew hard and somewhat deformed from sitting on its heel in gunsafes, and did it a bit faster than most other rifles. The stock design was very comfortable for me, but its style was not as graceful in appearance as some others.
The Sako integral-groove receiver demanded the use of rings designed for it. The front ring could be slid forward or backward a short distance, which allowed some slight windage adjustment in the mounting of the scope, but unless the rings had polymer inserts that could swivel slightly and allow for this adjustment the scope would and could suffer some torquing if too far from perfectly centered. I forget which rings did and did not have those inserts, but I consider them a must if using rings that clamp directly to the grooves. You can always use the OptiLock bases and rings, but IMHO bolting a separate base onto a receiver grooved for direct attachment of rings just seemed wrong...inelegant.
My last Sako was an AV-actioned .338WM; sold it only because I finally found the perfect .338WM Win70 Super Grade that I had always wanted. I've gotta say that the Win is, to my eye, far more attractive in appearance, but in terms of mechanical function, trigger, accuracy, etc. I still think the Sako was a slightly superior rifle.