I would spend some time hanging out on eBay looking at Weller and Rookwood. Neither of them made your vase but sellers like to suck you in and you might find something similar. That would give you a start. Also think about who else made free hand decorated brown ware – JB Owens, Cambridge Art Pottery, early Roseville, early McCoy (Loy-Nel-Art) and some of the Cincinnati shops. I don’t know that it was any of them but you might find a similar shape (a hobbyist could have purchased a blank and decorated it at home) or you could find a listing that says “This looks like ______ but it isn’t.”