Voltage increase when connecting a large load to household circuit
This seems like the neutral cable in a split 120-N-120 service is not handling the full current. A small gain in brightness of a lamp on one side of the circuit, when a 30 or 50 A load is applied to the other side, is not unusual, but measure the voltage if it's more than a barely-noticeable increase in brightness. The maximum voltage should be no more than ~127 V.

In the extreme case of a neutral wire breaking (which happened to my service after a tree fell on the entrance cable), the voltage across each half of the circuit becomes 240V split by the resistance for the circuit. E.G. with a 40 A designed load (3 ohms) on one side, and a 1 A designed load (just a 120 W lamp, 120 ohms) on the other side, the actual voltage across the lamp would be ~234 V, and the 40 A water heater would get only ~6V. The lamp would be very bright for a very short while. (In my case, I was lucky -- a few lamp ballasts burned out, but over-voltage protection varistors on outlets blew circuit breakers before a fire started).