Tilling that soil will bring up long dormant seeds of many kinds, and everytime it is tilled will bring up more. I would not concern myself with eliminating any "weeds" you cannot see and simply till the compost in (if that is necessary) and lay down a good mulch which could help prevent any new "weed" growth.

I agree with kimmsr, which doesn't happen very often ;-). If you put down heavy mulch, you would suppress most new weed growth.

For additional weed suppression many gardeners put down thick layers of newspaper, wet them and cover them with a nice layer of mulch.

Then newspapers don't last forever, but they do a great job of weed suppression in new beds. And then continual applications of fresh mulch every year or two should suffice for continued weed control.

Depends on what weeds you have but, in general, I do like to "pre-disaster" some sites by letting that first flush of weeds germinate and then finishing them off. But that method should only be used if you can dedicate the appropriate amount of time and attention to the site. Otherwise, mulch it immediately. Smothering should work with most weeds.