Subject: Why the number of molecules a constant, under same external conditions ?

Hi,
As per avagadros law, the number of molecules in a constant volume is the same, 
irrespective of the gas used, under same temp and pressure. As per my 
understanding, pressure is force exerted per unit area, i.e. the force exerted 
by molecules hitting on the box. Since one of the components of force is the 
mass of the body, shouldnt different molecule sizes mean different pressures 
for the same number of molecules ? 
The only answer I was able to come up with was that larger size means slower 
movement under same pressure, which will subsequently mean, lesser pressure, 
since the number of molecules hitting the box is lesser in unit time. But I 
wasnt completely happy with this answer. Can you please provide me the answer?
I would be much obliged if you can do the same.

Re: Why the number of molecules a constant, under same external conditions ?