Its an earlyish four screw K22 (its 4th screw is in front of the trigger guard).
The reason it is heavier than a 6" M&P is because it has a barrel rib and much smaller bore holes.
The 6" K22 was weight matched to the 6" K38 which has a much wider barrel rib , the same rib is used on your Model 66 but that also has an ejector rod shroud adding weight.
Shortly after yours was made it became known as the Model 17.
The stocks are correct style for your guns era, most had the serial stamped inside the right panel but sometimes a set has no serial.
On a side note,
S&W uses the term "Yoke" like the thing you put on oxen to pull a plow, generally Colt guys say "Crane" but that usually makes the S&W purists cringe.
The K22 is still produced today in stainless steel with a full underlug as the 617 or half lug barrel as the 617 Mountain gun which cost a little over $1k.
Cosmetic condition is everything in a collectable gun not so much as a shooter, yours is well worn and so in shooter condition, guessing it was carried in the field in a holster for quite some time.
If it has no mechanical issues it might tempt me if priced below $500, (the more the better as a buyer) but I have a few of them already.
A few years ago I found a slightly older one in about the same cosmetic condition for around $350 and was very happy to buy it.