Well, both Yiddish and German are listed as sources of the word, and Yiddish is Germanic and originated in the Rhineland, so it's more than likely that one borrowed it from the other. I just haven't studied Yiddish, so I'm more inclined to relate the word to German.
According to the OED, both spellings are acceptable; however, the date of the first use in English is listed as 1922 in Joyce's Ulysses, and it is spelt with two p's. Of course, if one is using it as a noun, the date of the first use is 1964 in The Economist and is spelt with only one p. In the end, it is obviously a matter of preference, and personally, I prefer two p's because that seems to me to be the root of the German verb schleppen. Also, as Kaichi noted: it feels more labourious that way. *grins*