I never thought this word through either, though it makes perfect sense that it would have to do with weight, both literal and figurative.
To make heavy or heavier; hence, to put weight on; to add weight to; to add apparent weight or importance, to exaggerate.
I. To put weight upon.
1. trans. To make heavy; to load, burden, weigh down; hence, to cumber, impede, retard. Obs.
b. To load (any one) with. Obs.
2. To load or heap anything heavy upon. Obs.
3. trans. To lay to the charge of any one; to bring as a charge or ‘gravamen’ (against). Obs.
4. absol. To bring charges (upon). Obs.
II. To add weight to.
5. trans. To add weight or intensity to; to strengthen, increase, or magnify. Obs. in gen. sense.
6. esp. a. Of things evil: To increase the gravity of, to make more grievous or burdensome; to make worse, intensify, exacerbate.
b. Of offences: To make more heinous, or offensive; to increase in offensiveness.
7. To exasperate, incense, embitter (a person); famil. to provoke, arouse the evil feelings of.
b. To irritate, inflame (physically).
III. To add weight unduly.
8. To make the most of; to represent (a thing) as graver, more serious, or more important; to exaggerate. Obs. exc. in extension of 6.