A friend and I ride belt drive bicycles. They work fine. Neither of us has experienced any durability problems. There's no need for lube, and I rather like never having to wipe down a chain.

Back in the late 1980s I owned a belt drive motorcycle. Owned it five years, rode it often, and that belt was still going strong when I sold the bike.

Weight is a tricky question. Belts require hub gearing, and geared hubs aren't really aimed at the weight weenie market. Whereas one can throw money at high-end derailleurs and hubs and cassettes, and even those chains with holes punched into the side plates, and possibly end up with a lighter weight drive train overall.