The pattern suggests cotton blends, cotton lawn, chambray, crepe de chine. I think cotton might be too stiff and cotton lawn too floaty.
Cotton is a fibre, not a fabric as such. Cotton fibres can be made into the finest of voile through to the heaviest of denims and furnishing fabrics.
You are looking for something a bit finer than most craft/P&Q cottons but not so fine as to be see through, so I concur with the others who suggest shirting fabrics; in cotton or cotton-viscose. Sometimes that is described as poplin, which (should) mean that the weft threads are softer spun and therefore loftier, than the more twisted fine warp threads.
It's difficult to judge the weight/handle of a facric if you have to buy online. it would help if the sellers would tell you gsm of the fabric but alas most don't
My Fabrics is good in that respect,
this is a selection from them, most of which are likely to be right sort of weight about 120-140gsm. Lots of other sellers out there too.