Nice view!
Extremely overbuilt upright posts. This appears to be adjoining 4×4’s and 2×8’s to form the posts. Its quite heavy duty, and likely overkill to meet the windzone requirements.
2×7 or 2×8 horizontal member to carry the roof. This would also be called a carrier beam. Sizes vary based on windzone, and size/shape of enclosure.
Learn more about this picture window screen enclosure from the ‘hotspots’ in the image above. Discuss it in the comments below!