It's as pointed out above electrical noise, from the lamps that produce this problem.
Not the bulbs, but low quality ballasts and transformers, some are worse then others, so it's the internals that can cause issues.
changing them to digital versions, will eliminate it.
Keep the scale and light on different circuit breakers,and use magnetic ferrite cores on the scales powercord, a few dollars a piece.
And you should have no issues.
Air currents and temperature changes will effect the scale too though.
Mijp5 all the lights driven on common, 120 v AC/ 60 hz grid as in the US.
Has a strobe effect of 60hz, it's just too fast for us to see it, except from fluorescent lights, just as with the European 50 Hz system.
So it has nothing to do with the issue.
And any welding, is best to avoid along with any sensitive electronics, welding is pretty much a electrical shortcircuit used to weld the steel these days.