Those 2xs, are they on 16" centers? Were you planning on parking a
truck up there, or do you just like the heavy, bulky look?
Will there be snow loads to contend with?
2x10 is standard for a 14' span to hold up a plywood and shingle flat
roof in house construction, but there you have 4 bearing WALLS. If you
want posts in the corners only, I would think about 4" pipe, buried at
least 4'. You're gonna need decent size beams from corner to corner.
How about picking up a roofing or framing book from the library for
ideas? Unless you get an answer here from a qualified architect or
engineer, you may want to think twice before building and risking
children's safety.