Your mechanic tells you that you have a weak cylinder but is not certain why?
Some more info about the vehicle would help, but if you legitimately have a weak cylinder (low compression is generally what this means) then you should have a slightly rough idle that may smooth out (depends) when the throttle is opened.
If your mechanic did not perform a compression test then he’s wild guessing.
Low compression is usually caused by piston rings, cylinder head valve, or possibly a faulty head gasket.
Any of this is easily diagnosed.