What is YDNA? For complete information on YDNA I suggest you go to http://www.familytreedna.com/ or just search on YDNA.
Simple put your YDNA is past down from father to son thus it's a great tool for finding direct male ancestors. There are huge databases of YDNA results from all over the world. That's the good news. Unfortunately, even though the Weeks surname is fairly common there are only a hand full of Weeks men who have taken and posted their YDNA results. The smaller the database the harder it is to get good result.
If you are a Weeks male please have your YDNA tested. The larger the Weeks sampling the better the odds are you will be successful using this technology to find your male Weeks ancestors.
There are few sites that have a YDNA Weeks Surname Group. They are:
http://www.familytreedna.com/ The Family Tree DNA Weeks surname group is managed by a gentleman that has a wealth of information on early Weeks families.
Sorenson Molecular Genealogy Foundation aka SMGF
If you decide to get your YDNA processed, I encourage you to test for as many makers as you can afford. I'd recommend a min. of 37 markers but more better.