wolman is treated wood, so I just used that name as I am familar with his products.
the 2x6 under the roof rafters could work if you have that much room and can handle it. I think you said your width was 14 feet. I would sink 6x6 posts in the ground at the outer width, then carriage screw a 2x8 on each side of that post and then let your 2x8 rafters from the ledger lay on top of this beam and again fasten with Simpson Ties. Place the roof rafters every 24 inches on centers. This should be sufficent. Make sure you build in a good slope rate to shed water and ice and snow.