Why have different departure hall and arrival hall locations?
I'm not sure if 'most' airports have this design. I've seen both cases (i.e. departures below arrivals and the other way around). Atleast for small airports, a few reasons come to mind for having departures above arrivals:


If arrivals is on ground floor, the baggage can come easily from the aircraft. This reduces complexity, especially in small airports.
Most of the aircraft are boarded using jet bridge- makes sense if they are boarded from first floor (or above); of course, jet bridges can also be used for disembarking, so this is questionable.
The upper floor offers a good view to enjoy while shopping or eating. This maybe the reason as more time is spent in departure. Also, if the arrival is in ground floor, one can simply 'walk out' as no checks are there (international flights are a different case).


None of these arguments are convincing, I guess.