I bought my 1st synthetic aftermarket stock in 1982 and haven't hunted with wood in 30 years other than an occasional trip with one of my leverguns. Even the cheap plastic stocks are much stronger and stable than any wood stock and at least as accurate despite their flexibility. The cheap stocks are no lighter, but a quality aftermarket stock can knock 1/2-1 pound off the weight of your rifle.
The biggest advantage is stability. Waterproofing a wood stock is an excercise in futility. You won't suceed, and even if you do 10%-20% of any stocks weight is made up of moisture trapped inside the stock. When the wood is kiln dried they leave that much moisture in the wood. Any less and the stock would be so brittle it would break like a matchstick.
Even if perfectly sealed this internal moisture will expand and contract as environmental conditions change causing the rifles point of impact to change. You don't have to be hunting in the rain. As seasons change there will be changes to your stock with it setting in your safe, in your home. Zero your rifle in August at 500 ft above sea level then take the rifle out in November and hunt at 7000 ft above sea level and you may well find that the rifle still shoots 1" groups, but that the 1" groups are 3" to the left of where they were in August. If you never travel to hunt, and the humidity is low and pretty stable where you live this is less likely to happen. But the greater the swings in temperature, humidity and altitude, the more likely you are to have problems.
Point of impact changes are the biggest problem, but I have seen wood in rare cases split and crack because of environmental changes. A hunting partner once noticed a 1/2" long crack in his stock directly behind the trigger guard on a rainy morning. By lunch the crack extended all the way to the grip cap and was almost 1/4" wide.
My personal motvation for a quality synthetic is weight reduction. I went on my first backpack hunt in 1977 and back to the same place in 1980. Made up my mind then that I wouldn't be going back into places like that again carrying a heavy rifle. I was just out of college and broke. It took me 2 years to save up the money, paid more for the stock than the rifle, but it reduced the weight by almost a pound and made the gun much more consistently accurate. I have only recently retired that gun, but all of my serious hunting rifles now wear McMillan Edge stocks that are considerably stronger and lighter than wood.