Weekly challenges refresh at 7PM PST Saturday, 10PM EST Saturday, or 6AM Sunday GMT.
(That might be one hour later depending on where you live and what Daylight Savings Time is currently--when I wrote the solution it was the earlier time, currently it's the later time because of Daylight Savings Time)
They are readily accessible from the Main Menu, at the bottom of the screen under "Challenges".
The challenges I've had so far are fairly easy, just more time consuming than the daily challenges.
Examples might be:
"Play 9 match-made games with Decimus"
"Get 50 Counter-kills in match-making"
"Win 2 match-made games"
Once you complete a weekly challenge, it will show you the countdown until they are next available.
There is a potential good glitch with this--you might get the achievement when you've only completed 1-2 of the weekly's even!