Two obvious possibilities: carbon build-up in the muffler due to over-oiling the fuel by the previous tenant, or fairly severe blow-by due to scored piston or bore, or worn rings. You can check these things fairly easily. Remove muffler and compare its weight with a clean one, or temporarily substitute a clean one and see if the smoke goes away. While muffler is off, inspect the side of the piston for scoring, by looking through the exhaust port. To check condition of rings, check compression in comparison with another similar engine by pulling the starter cord with spark plug disconnected. Then put a spoonful of oil in through the spark plug hole and see whether compression increases.
