PROVEN: Marijuana messes up your sleep cycle by disallowing you (or allowing you much less often) to go into the REM portion of your sleep cycle. This generally sticks around until you've been abstinent from weed for at least a couple days.
PROVEN: Marijuana is less chemically addictive than alcohol or tobacco. Just like there are plenty of people hooked on caffeine, weed addiction is more about lifetsyle or your personal psychology than about actual chemical dependence.
UNPROVEN: Smoking weed has a correlation (not necessarily causation) to a decreased risk of some kinds of cancer. Research think this may be caused in part by cannibinols in weed stimulating growth of the white blood cells that fight cancer cells.
PROVEN: THC in marijuana prevents the formation of deposits in the brain associated with Alzheimer's disease. THC was found to prevent an enzyme from accelerating the formation of "Alzheimer plaques" in the brain
more effectively than commercially marketed drugs. A 2012 review from the Philosophical Transactions of a Royal Society B suggested that activating the cannabinoid system may trigger an "anti-oxidant cleanse" in the brain. The review found cannabinoids may slow decline in age and disease-related cognitive functioning.
Basically, there's a lot of good shit weed does and most of the bad shit that it does is caused by the actual smoking of weed itself (if you smoke it rather than eat an edible or vaporize it, it has a lot of the same tars in it that cigarettes do). There are also a few studies suggesting that marijuana use is correlated with psychoses (such as schizophrenia) but more likely its just that people with psychoses are more drawn to smoke weed.