lumber sizing for covered walkway

I'm putting in a covered walkway on the side of my house & am wondering about the lumber sizing. The cover is a simple clay tile roof, 9 1/2' high, 3' wide and 30' long, supported by the house on one side and three or four posts on the other.
Here's the plan, bottom to top:
three 6x6 posts spaced at 4', 13', 30' (there will be a 4' overhang) two 2x10s on top of the posts 16 2x6's, spaced 2' apart to hold the roof decking 3/4'' plywood roof decking tar paper tile
The question is: are the three 6x6 posts sufficient or should I add a fourth? I'd rather add another post than use fewer, larger ones so I don't block the walkway.
Kyle A. York
Sr. Subordinate Grunt
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