Stop operation and arrange assessment of both the appliance mounting and the sink support. Visible movement of the sink changes the problem from a noise complaint to a question about the complete supported assembly.
What the observation tells you
An undermounted or otherwise supported bowl should not be repaired by pushing up the disposer from below. Do not add wedges, hang extra weight from it or reproduce the movement for a longer video. Note any separation, cracked seal or recent work without disturbing the area.
A useful next step
Keep the affected sink out of use if its security is uncertain. Explain the sink type and mounting access when arranging assistance.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.