I was curious about this today, actually.
I was looking at the stats under the character in the C menu and the only thing I saw change was the Damage stat. I was confused by the numbers, but after reading that it shows the full range of the lowest to the highest of either weapon, it makes sense.
The things that confuse me are the following:
I was thinking that the left and right mouse buttons were linked to the left and right hands, but this does not seem to be true. The only thing I can figure is that it's set up to allow you to link skills to each left and right mouse button, but the actual skills use different hands in different ways...?
Using a single 1H weapon in the main hand gives it's Damage range as normal. Switching it to the offhand makes all the skills reliant on a weapon red and unuseable, which is confusing. So, it favors the character's right hand for the skills, and the left hand won't allow the use of skills.
I tested three different 1H weapons in each hand, and I did see a noticeable change in my toon's attack speed when holding down the mouse buttons. Since I can't find a practice dummy or a monster that doesn't die in two seconds I can't test and see actual damage numbers.
What does a second weapon in the offhand (left hand) actually do?
I don't have enough different skills to test since I'm a noob, but any enlightenment would be greatly appreciated.