I think of 'tarry' as hanging around because you want to be where you are and don't really want to go go elsewhere, even if you feel you should go.

The meaning seems well demonstrated in the song Journey Home

No time to tarry here; no time to wait for you
No time to tarry here; I'm on my journey home

Marvelous song for group singing, since the solo part consists of one noun ('mourners', 'sinners', 'sisters', etc) at the beginning of each verse.

I note (haha) there is no tune.