First: There is no current NIJ specification for III+. It’s either IIIa, III, or IV. III+ is a marketing gimmick for plate that stop all level III threats, but don’t stop all level IV threats.

Second: I guess that depends on what you count as ‘prohibitively heavy’. UHMW plates that are listed as III+ by the manufacturer (again, there is not NIJ specification for this) can be in the 5# range per plate for a small. My backpack in middle school was easily 25# since I never used my locker, so ???.