One definition of "heavily armed" is "armed with one or more heavy weapons". A "heavy weapon" or "heavy arm" is one that isn't a "light" or "small arm".
And from typical definitions of "small arms", that would imply that being armed with a "heavy" machinegun/mortar/rocket launcher, any other crew-served weapon, an arm so "heavy" a single person can't carry it, or an arm with a bore of 20mm or more would count as "heavily armed".
In keeping with the Foxworthy approach (good idea, Billll!):
You might be heavily armed if:
... instead of a carry permit, you need a trailer permit.
... your reloading press is a log splitter.
... your gun cleaning kit includes a garden hose.
... a "nice" range is one with an impact zone over international waters.
... the money you save on Pelican cases goes into winches and rigging.
... your shooting buddies have nicknames like "Loader" and "2nd Assistant Gunner".
... you use ammo crates instead of cans.
... the range rules include "shooters are responsible for towing away burned-out vehicles"
... recoil isn't an issue, but "sustained rate of fire" is.
... you use your wife as a "forward observer".