If the spark plugs are old, replace them.
Ignition coils (on top of the spark plugs) age and cause the same kind of poor performance as bad spark plugs.
The intake rubber boot can crack and cause poor performance. For me it did and when accelerating, the engine twisted slightly to widen the crack.
If there is no difference driving the car with or without the air flow meter, something is wrong. Either another bad AFM or bad wiring to it.