Glass does indeed behave as a liquid. But the differential thickness of old glass panes is to do with how they were made and fitted together rather than age. The flow rate of glass is so slow that glass is never in one place long enough to show appreciable thinning.
Although it is technically a supercooled liquid (it has no grain structure and is perfctly elastic up to fracture), but it does not flow. Old glass can sometimes be thick at one end than the other, but this can occur at the top and side of a pane of glass, not just at the bottom. This is because of how the glass was made, rather than the fact that it 'flows'.