Tom: You're not too far off. A heavy arrow will quiet a bow and reduce its hand shock, of course. And, that's the reason (and reason enough IMO) a lot of folks like them. As Widow eater illustrates, " My bow likes heavy arrows because I like heavy arrows." It's generaly agreed that heavy arrows also penetrate better than lighter arrows, other things being equal.
John Havard has addressed this issue in the past based on a lot of testing he's done. In short, he notes bow efficiency is bow efficiency. A bow that shoots a light arrow slow also shoots a heavy arrow slow. Likewise, a bow that shoots a light arrow fast also shoots a heavy arrow fast, not as fast as the lighter arrow but also fast.
Sometimes, when folks say their bows like heavy arrows, they're implying that their bow shoots a heavy arrow faster than a light arrow. Never gonna happen.