The faucet should swivel where its design allows it, not rotate as a complete assembly every time you move a frying pan. Put a small removable mark beside the base and watch it during gentle use. This is an observation, not a strength test.
Watch the handle, body and sink separately
If only the handle rocks, its connection may need attention. If the whole body slides against the deck, look at the mounting below. If the body stays fixed to the steel but the steel dishes up and down, the sink deck itself is moving. A countertop that feels soft or shows swelling changes the job again.
Handle moves alone
Identify the handle assembly before touching its retaining screw.
Body slips on the surface
Inspect the correct mounting hardware and how it bears underneath.
Surface bends with the faucet
Assess the sink deck or countertop; more tightening may not help.
Give the mounting hardware enough room to be inspected
Empty the cabinet and use a light and a phone camera to see behind the bowl. Note missing brackets, displaced washers, corrosion, wet wood and hoses wound around one another. Do not pull the faucet around from above while its hoses twist below. If the cabinet is wet, deal with the source of the water first.
Moen: Side-mounted handle and mounting hardware distinguishes the handle's retaining screw from mounting hardware beneath the sink on the handle style it covers. That distinction is useful; the screw arrangement is not universal. Find your installation drawing, including any deck-thickness limits and specified support plate, before making adjustments.
Tightening works only when the parts can clamp properly
A suitable mounting bracket must sit against sound material in the orientation shown by the manufacturer. A nut bottomed out on its threads, an incorrectly stacked washer or a bracket caught on a hose can feel tight without clamping the faucet. An installer can identify that quickly with proper access; force from an awkward angle tends to hide it.
Thin sink decks may need a compatible reinforcement arrangement approved for that sink and faucet. Swollen particleboard needs its moisture damage assessed. Neither condition is repaired by a bead of silicone around the visible base. Avoid improvised screw holes through a sink or stone counter.
Use it normally, then look underneath again
After the mounting is corrected, check the full spout and handle travel, watch the hoses and inspect for fresh dampness during normal use. A base that loosens repeatedly deserves a cause, not a standing appointment with the wrench. If the handle is fighting the backsplash, check its movement clearance before blaming the mount.