Someone posts a thread like this every 3 weeks or so, and I get tired of posting the same old things, but people should really hear these bands:
White Mice (weird, not for everyone, but definately no guitar.)
Olneyville Sound System (We're all in it Together is better IMO)
Noxagt (Their first two albums;"Iron Point" and "Turning it Down..." only, after that they lost the viola)
And I don't know about heavy, but
Wizardzz is definately pretty epic in a classic 16-bit sort of way.
And DFA1979 really isn't that heavy; loud, maybe but not heavy.