Hi A Squared,
The pressure differential for a constant velocity will be proportional to the density of the air.
I agree.
JSeward, try putting some actual numbers into the relationships I posted in #2.
Assume your carburettor is set up for sea level with the jets and needles etc. all set correctly.
If you now fly where the density altitude is only half that at sea level, and develop the same engine power by doubling the speed of the airflow through the carburettor (density * Velocity of air through the carburettor: 0.5 * 2 = 1), then the pressure drop through the carb's venturi is now double what it was at sea level (density * V*V: 0.5 * 2 * 2 = 2). Therefore about twice as much fuel will be sucked through the petrol jets than is required and hence you will have to lean the mixture off.