Curtain rod suggestions for two sets of heavy curtains layered on top of each other?

Yes, if you have 2 sets of curtains to open (typically 1 2-piece drape and 1 2-piece sheer), it has to have a double curtain rod made with 2 pull trolleys on each rod.  You pull it open with a cord and it opens from the center to the sides.   You can open the drapes and leave the sheers closed., etc.  You have to use the double rod because there is no way to mount the rods to the wall without the rods and draperies being custom fitted specifically for that window.  By opening in the center, the rod will have a center support, so the span will be about 5 feet, which is not bad for a drape.  Dimensionally, 2 separate rods will not fit and look right.   For your situation, use your material to make custom draperies, being aware that you may not be able to get 2 draperies back to back without hitting each other.  If you open the window drape it may hit the other drape and pull it back.  That is why the window side is a sheer. I would suggest you find a custom draperier and use their expertise.  Let them furnish the rod and let them make the drape using your material and install it.   If you are trying to shut out any light by 2 drapes, consider 1 drape and having it lined with another material when they customize your drapes.   

They do sell the dual rods but for that weight id do 2 rods.

This is hard to explain but, rods have a width measurement inches away from wall..while some mount close to wall or inside frame...

Look online pottery barn, jc pennys, at their curtain rods and sizes...youll find the look you want then...check size..measurement of dual rods

Id use better screws than what comes in the rod package.

Another thing to consider is the pocket size where you slide rod...if you will open close a lot you want it large to move across rod. They have new curtains that have holes for rods and they work great to move often.