Moen 2-stem kit. Faucet's flow pulsates on low flow and the sprayer dribbles. Increasing the flow stops both. What is my problem? What fixes it?

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Increasing the flow stops both.

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What does that mean? Does it mean the pulsating stops or water flow stops?
Remove aerator from the faucet spout and see what happens. Remove the spray head and see what happens?

If you mean the pulsating stops then you probably have a loose washer in the stop valves. Does the pulsating occur hot, cold or both. It would be unusual to have a loose washer in both hot and cold at the same time. Close stop valves then reopen and see if pulsating continues.