Only 1/16" body

A midge or gnat comes to mind, but those do not typically hunker down in grass, unless they are being flushed out very early or late in the day. Certainly not a crane fly, a known pest of lawns.

Do you have dozens, or hundreds?

With every step about 5-10 fly out so across the whole lawn maybe a couple hundred. Would midge or gnats cause stress to the grass?

No. And your infestation is not particularly dense, unless it is still increasing. I would think nearby lawns would have these also, unless your lawn has been newly sodded.

see: leafhoppers