But in terms of performance, those 2 machines don't really compare, do they? They have roughly the same seating capacity (737-400 a little smaller). But the A320 offers substantially more range because it has a much bigger (more efficient) wing with much bigger fuel tanks contained therein. The 3000nm range criteria set for the A320 means that the bigger wing is necessary to accommodate the required fuel and I'm sure that's where you'll find the bulk of that weight difference that you quote - in the much bigger wing.
That along with, of course, the fuselage which is both longer (slightly) and wider (slightly). That adds up to quite a lot more metal in the fuselage as well.
p-k-b