Are 2x6 rafters adequate to carry a day bed in a pergola?

I’m working on my first big project, a 10×16 pergola. The long side includes three 6×6 posts 8 ft away from each other. There is another row of 3 posts 10 ft away parallel to those posts. All posts are set below the deck on concrete footers and deck posts. Posts are notched on top to receive 2×8 beams.

I have 2×6’s running the 10 ft length underneath the beams to give some stability. My wife was wanting to hang a rather large swinging day bed from the pergola on the side where the grill is next to the fence. It will be about 5ft 6in wide and weigh about 75lbs. I would want to make sure 3 people will be safe on it just to be safe. So the overall load would be around 650-700 lbs. It would be attached at two different points across the length of the rafter above where the bench armrests would be. I can either make it hang from two ropes on one rafter or four ropes attached to two different rafters like the pictures I included, whatever is necessary. I was wondering what size rafters I would need to support that kind of weight if it’s spanning 10 ft. I currently have 2×6’s bought for the rafters but from what I read I will need something bigger.

I would prefer to avoid 2×8’s just so the top doesn’t get taller. Would 4×6’s work as rafters? Thanks for the help. Pictures attached in link of ways I’m looking to attach the swing.

More photos