This is an entry on its own in the Mesa Grande dictionary defined simply as, "kept coming". Weyiw (neyiw) is "comes" and nyim is apparently short for nyimvey, "anyway, somehow, always".
In the recording, Cuevas then corrects to nyimvey weyiw, which is probably to him the more natural way to say the phrase.
One can presumably switch out weyiw for other words, such as nyim wemii, "he kept on crying", but this has yet to be proven by documentation.