He didn't mean Nate was heavier than him.
He meant that he's used that people in featherweight/lightweight fall from such hits he had thrown, while a heavier man like Diaz could take them, which Conor didn't expect.
Maybe, it sounded like he was implying Diaz was heavier than him in one of the things he said, but I guess it could be either way. Diaz brothers are known for their good chins, so it really shouldn't have come as a surprise.
Either way, Conor is the most entertaining fighter in the UFC right now, with his agile always-finishing fighting style. He needs to fix the holes in his games, biggest of which are: lack of jab, lack of lead hook, lack of orthodox stance even when in trouble, lack of Muay Thai style leg kicks, and his tendency to block shots with his chin. Regardless of what some people say, it has yet to be proven that ground is a problem for him.