It isn't part of my dialect. But it causes me to notice that there is a large overlap between prepositions & adverbs in English: "up", "down", "around", "about", "along", and many other can be either. The thing has ragged edges, as most things in language do: consider the cases of in(to) & out (of). Thus, it is rather an oddity, but not surprising, that in standard English "with" cannot be an adverb (one has to use "along" instead); but neither is it surprising that some dialects have filled in that hole.