Rep isn't carried over anyway--all the SE sites have a different rep counter/badge counter for your account. (Though site metas display the same rep).
Rep on each site is independent for a reason. Each site has its own set of niche rules and policies, so being awesome on one site does not make you eligible to get privileges on another. The rep is a measure of how much people on that site trust you.
What linkage does:
Shows all your accounts, ordered by rep, in the accounts section of your profile on any site:
Shows your accounts on your SE profile accounts tab
You get +100 rep on every associated site (and every site you join thereafter) once you reach 200 rep on a single site. You get +100 on that site as well. This bonus is so that you can get past most of the newbie barriers on a site.
Shows combined rep on SE 2.0 site chat
It also combines eligible accounts on your combined flair. Unfortunately, you don't have enough rep on any site to own a combined flair; all you get is this : (More details here).
Example of how combined flair looks: . Note all the site icons on the bottom.