Whether or not uwig is commonly regarded as a German word I'll leave unanswered, but for uffig we first need to find a definition. Perhaps due to words like affig or puffig it sounds somewhat derogative to me, furthermore uff is the canonical interjection for indicating physical exhaustion, so it could be a slang term applied to very straining and exhausting tasks.
That is a seriously disturbing image. "Uffig" may be ancient slang, but is definitely a word that I used to hear quite a bit when I lived in Berlin in the late seventies. As I recall, it meant something along the lines of "lästig", that is something that was a pain in the rear to do, and was probably not worth the effort. annoying, irritating, aggravating.
I acknowledge, however, that it is not in the fine online dictionary brought to us by the good folks at the T.U. Chemnitz. But I do not believe that I made it up.
But here is a paragraph about Poker on wikipedia, in some vaguely Germanic dialect, where it appears:
Bi me Pokerschpil wechselt sich s Tusche vun de Karte mit Wettrunde ab. D Onzahl vun dr Wettrunde hangt vun dr gschpilte Variante un de Onzohl vun dr jewyls verteilte Karta ab. E mänkmol werre au Karte uffig un/oder fir alli Schpiler gmeinsam usteilt. Gwinner isch derjenigi Schpiler, wu im Showdown di beschte Karte zeigt, oder wu als einzige nit usstygt. In däm Fall muess derjenige syni Karte nit vorzeige, mer brucht en Bluff also nit zuezgebe.
It was probably Munich... I live comparatively far to the left of Berlin where I hardly ever come in touch with this city's eponymous slang, but even my parents have never heard that word. In Bavaria however (though in Munich somewhat less I've heard) they speak this utterly different language—if they are really good at it I won't understand a word—so it's very possible that it is/was a common slang term there.
It yields a few thousand Google hits, but hardly any of them seem relevant.
(Oh, and I forgot to mention knuffig, such a cute word.)
This Wikipedia article is from the Alemannic Wikipedia. Quite intriguing.
(Only I'm afraid to think too much in German at the moment due to an English test I have to take in about a week...)
Edit: Guessing from the context it seems uffig means as much as open in Alemannic.