In at least one news story of the LAX shooting, the perpetrator Hesham Hedayat is held to be "heavily armed". Two sidearms and a knife? There's a reason they're called "sidearms."
In contrast, Chris Bray explains in a Reason article how the press poorly understands the military:
"U.S. infantry units of every type tend to be grouped in rifle companies of 200 . . . armed in part with machine guns and grenade launchers . . . The very thing that distinguishes the Rangers, if you’re inclined to be picky, is not that they are more heavily armed than other infantrymen, but rather that they are often less heavily armed . . . "Emphasis mine.
So a force of 200, carrying company machine guns and grenade launchers (in addition to individual weapons such as carbines, sidearms, and yes, [shudder] knives) is lightly armed. But one man carrying two handguns and a knife is heavily armed.
To be fair, it is a question of context. Hedayat was carrying more armament than people usually do in LAX (whether that is true in comparison to the Los Angeles area as a whole, versus the airport, is another matter). He was probably carrying no more than the El Al security were---backup handguns are common, as are folding knifes, in that field.
The meaning of this term has been dulled to cliche by careless usage, much like hard-earned dollars, law-abiding citizen, or unarmed women and children. I humbly propose a moratorium. Just stop writing heavily armed when simply armed will do.