Somebody smarter than me will hopefully chime in, but this looks like the spindle servo is dithering. Either it's hunting for an encoder position and is falling in between pulses, or the PID settings are causing it to move between a couple of positions. The heavier the part, the more inertia it has when the servo 'corrects' the position - it then overshoots and gets corrected back. Looks like an improperly tuned PID setting.
If you haven't changed settings on the servo drive, then my first thought is that there's a mechanical problem with the spindle servo encoder. Perhaps you can check the encoder to see if it's mounted properly (clamped on motor shaft square, tight, and the anti-rotation tab isn't loose).
If you have changed servo drive parameters, then you'll need to discuss this with someone more expert than myself on what parameters (P, I, or D) to change to reduce dithering or hunting. You might get more responses on the CNCZone "Servos" sub-forum.
If you haven't changed drive parameters, and everything looks tight (including electrical connections), you still may have a servo drive issue. Your operator reported this has happened in the past - if you've only been milling small, light parts since day one, this may be a drive setting problem right from the factory that has only become very noticeable with the larger part.
Again, check the encoder first, then re-post in the servos forum if you want some expert help diagnosing and tuning the servo drive parameters.