My guess would be:

A "Light" truck would be something like Mikes: full bodied pick up, limited armor (just 2 bumpers and sliders), smaller tire size, aluminum or steel wheels, etc...

A "Heavy" truck would be something like a 4runner, with full armor (bumpers, sliders, full exo or internal cage), big tires, beadlocks, etc...

Plus I am assuming most of these statements being made about power on the 2.7 vs the 3.4 are based on an empty truck that isn't loaded with passengers or gear.

But I haven't driven either engine in anything other than a stock Tacoma, thats just my guess on the vaguest way to estimate if your truck is considered "heavy" or "light"