Adding a roofed area would be wonderful, as long as you don't lose too much light in the house by covering a window. Any more photos for ideas of the whole area?

This is another angle and full back view of the house. We get a lot of light into through the windows around the kitchen table (center) and side glass door. The window that would be blocked is over the kitchen sink, so that is a bit of a concern, but so much light comes in from the side I think it would be OK. I took this late afternoon (in March), so in the summer it is full sun most of the afternoon.