120 volt wiring problem
Sounds like a high resistance connection somewhere. Try plugging in both the 3-light tester and a light to the outlet. I expect that then, the tester will indicate something wrong. If all of the lights go out, the problem is on the hot. If it shows an open neutral, then the problem is on the neutral.
I’d suggest you remove the outlet and check all of the connections. Also, if you are using the back-stabs, you should switch to the screw connections instead. These are much more reliable.