There's more to a weapon than the cyclic rate, muzzle velocity and carried weight. Before the M249, there was an attempt to use an M16A1 with a bipod as the squad automatic rifle.

Machine guns take more of a beating because sustained automatic fire is hard on a gun. The M249 is heavier because it's built to handle that work. The belt feed also means a lot less time spent reloading vs a twenty or thirty round magazine.

Not that I necessarily have an informed opinion on which is the better choice, but I do believe the M249 is not completely irrational. It's simply a different set of tradeoffs.