I decided to test this by removing my gear and all increased attack speed. I then test the weapon I chose for my main hand, over 400 base damage with 1.60 attack speed. During Rapid Fire I was averaging 800 never below 450. I then tested weapon #2 which i later put in offhand barley over 200 damage and used rapid fire. I was averaging around 200, never over 375. I then duel wielded each weapon. #1 in main and # 2 in offhand. I recorded myself shooting creatures with short bursts of rapid fire. The outcome was this.
Barrage #4: 532, 649, 544 (crit), 490
Barrage #5: 80, 185, 84, 122
Barrage #6: 220 (crit), 1200 (crit), 823, 743
In barrage one you can see that all 4 shots were fired from the offhand due to none of them deals over 400 damage. In barrage #2 you can see all 4 shots are from the main hand, due to all the weapons damage being over 500, but in barrage #3 you can see both the main hand and the off hand dealing damage. the main hand being the 636 and the off hand being the rest of the damage in the barrage. In barrage #4 I believe that the main hand did all of the damage due to the fact the the off hand never crit for over 375. This also makes Barrage #4 mimic #1 but for the opposite hand. In #5 it is all off hand damage that mimics #2 except for the opposite hand and in #6 it is mixed again with the offhand dealing the 220 crit and the main hand dealing the rest, but still mimics #3.
As you can see each weapon has its own consistent damage. It also appears that each weapon has some sort of a cast time and a rhythm that barrage 1 and 4, 2 and 5, and 5 and 6 mimic each other, but is even. The only differences is which weapon was dominate in the set of attacks. If each alternate weapon did damage for each alternate hit the damage would look more like 800,200,800,200. I suspect that weapons with different attack speed would have a much different outcome, and the dominate weapon being the one with the most attack speed.