So if you don't have second attack, a really heavy sword and a really light are both going to get one attack / round.

If you have dual wield, second attack, third attack, or fourth attack, I do not know if weapon weight plays a factor in the check for those skills.

What you should focus on is which weapons are going to be parried or dodged less by your opponent. In CF, it isn't so much how many attacks you get, but how many of the attacks you do get land. Assassins get skills to help change these odds also. For example, the helpfile on dodge specifically talks about dex, so if you lower your opponents dexterity they dodge less. Most classes require a weapon to parry, so if you get them unarmed, they aren't going to parry. And so on.