Stumped about a receptacle
One possibility is that the contacts in the receptacle are corroded or burnt. Or there may be some other fault in the wiring or connections to that receptacle. Perhaps a loose wiring nut or an undersized conductor.

This would create a resistance. When no current is flowing, no voltage is dropped across the resistance - so you measure nearly full voltage. However when a load is connected and a significant current is flowing, a voltage drop will occur across this resistance.

This is of course a fire hazard. The resistive part will heat up considerably.

ratchet-freak's diagnostic suggestion is a good way to verify this - use an extension cable so you can simultaneously plug in a high-wattage lamp (as a test load) and volt meter. See if the voltage dips when you plug the lamp into the extension.