The weather is awkward, so thick knits feel like too much—are there any thin sheer knits?

There are no knits confirmed in the materials with the 'sheer (see-through)' material you mentioned. Instead, I picked three long-sleeve tops that are thin and light or have a lace texture. They are confirmed to be a lace jacquard knit and light, soft cashmere-silk blend knits.

I picked three knits confirmed to be short-sleeved. They are confirmed to be a 100% wool knit pocket top with a light, soft touch, and rayon blend tops featuring a lace jacquard texture or structural silhouette.

I picked three knits in calm, neutral tones like charcoal and grey. They are confirmed to be a light, sheer cropped short-sleeve knit, a merino wool blend short-sleeve knit, and a sleeveless top with a subtle pointelle texture.