In my meager experience I have found that the longer barrels shoot both RB's and shot better than shorter barrels, in all gauges, when they are properly loaded. With practice you can wing shoot with a 4' barrel, in fact if you don't mind missing a few you can shoot skeet with good success. But generally if you are only going to shoot shot I'd go with a 16 to 10 bore and keep the length to 36" to 42". If you are only going to shoot RB I'd go 28 bore, 48" to about 54", after 54" the gun can become inconvenient. Although with some experience you can learn to handle barrels out to 72" long. Also, don't associate weight with length. Properly built long barrels aren't heavy.
Historically, and I know many of you don't care about that sort of thing, English trade guns in the 1700's had barrels that were most commonly 4' in the barrel. Next most common was 3 1/2'. Through the first 1/2 of the 1800's the most common trade gun barrel length was 3 1/2' with 4' still popular as well as 3' becoming more popular.
French trade guns in colonial america had barrels that were 4 pieds in length, which translates to 53 1/4" . This length was pretty universal with French trade guns.
It wasn't unusual for barrel lengths to vary an inch or so in both French and English trade guns, usually on the shorter side of the variance. Small differences is actual barrel length didn't seem to matter back then.
English trade gun barrels were quite light in weight. The breech being about 1". A finished english trade gun with a 4' barrel weighs 6lbs give or take a few ounces. French trade guns commonly had barrels between 1 1/8" to 1 1/4. The original french trade guns with barrels 4 pieds in length I have examined usually weigh about 1 pound more than their English counter parts with a 4' barrel.