The plane will cut deeper wherever you put more pressure and vice versa...
This could also be a sign of a plane being concave from toe to heel. A simple test is to set the blade for a minimum cut using a small block of wood held in hand. Then set the plane on a piece longer than the plane that is known to be straight. Push the plane forward without downward pressure. If there is no shaving, then the area under the blade is off the work. To further test, push down on the plane on the same set up. If it then takes a shaving, concavity is confirmed.
jtk
"A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty."
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