Well first off, I would suggest that you go to the Machka's web page. Machka has some very good tips for riding centuries. Machka posts on this board and on the long distance cycling board often. Just click her name and hit the web site.
You are still young enough to get into shape relatively quickly. Doing a century in June should be attainable.
Riding 7 miles twice per day will give you some training during the week. But it really is not that much training. Still, any exercise you do is good and the more you do during the week the better (within limits of course)
I would strongly suggest that you increase your mileage on the weekends. The 35 mile ride was good start. Try increasing the mileage by about 10% per week. The rule of thumb is if you get in a training ride that is 70% of the distance of your target ride, you can do it. So try to work up to doing a 70 mile ride. Usually the excitement of THE DAY will stoke you enough to do it.
The main thing about centuries is pacing. Generally, just backing off an mph or two from your normal cruising speed will give you a good century pace. Or ride at a pace that is just a bit harder than you can hold a conversation at. If you end up feeling strong and want to speed up at the 80 mile point then you can do that. Having some zip at 80 mile sure beats feeling like a road kill at 60 miles and grimly grinding out 40 miles. By the way, I used to belong to a club that had an annual multiday ride that featured 4 centuries done on consecutive days. Some people did them every year without training! They just rode along at 12-14 mph and never missed an opportunity to stop for ice cream. Holy Calories Batman! They did it. You really don't have to be in great shape to do a century. You just need to know how.