I went with this Anker 10000 mAH battery at 6.4 ounces it's a couple ounces lighter than other 10 Ah batteries I've seen, and it's very small in size.

For solar I have a small panel from Sunkingdom that weighs 6.5 ounces on my scale. So a total 0f 12.9 ounces for battery and panel.

I used this same combo of solar panel and 10Ah battery on the colorado trail this past summer and found it worked well. Many days I would use the solar panel only, but it was nice to have the battery for the times it was cloudy for a few days in a row.