what size lumber for a 8' horizontal span to hold a 250 lb. load
Depends on 1) Species, 2) Grade, and 3) Condition of use (wet location, etc.)

1) Some species of wood are stronger than others, (i.e.: Douglas Fir-Larch is much stronger than pine,)

2) Some grades of wood can be 80% more than others. 

3) Wood, pressure treated, can loose 20% of its strength and if it’s installed outside in a rainy or high humidity climate, can loose an additional 15% of its strength. 

So, for your chair outside with 7’-6” span, I’d recommend 2-2x6 of “Select grade or better” or 1-2x8 of “number 1 grade or better”.