I can't, however, remember the lectures I attended where the subject popped up, so I might be a bit off...

I assume it is a matter of an effect much larger than the force of gravity between the plates could give rise to. (the plates would have to be of fairly low mass for a meaningful experiment on the topic anyway)

Or, as I don't know the precise details, it could be a matter of initially being a Gedanken experiment; where the plates are assumed to be massless. This does not explain the experimental results, though...

But most likely, it is due to the fact that gravity is weak...