Does 態々 derived from 態と? And does 態と derived from waza 「業 」and case-marking particle 「と」?
In modern Japanese, わざわざ and わざと are different adverbs. わざわざ mainly means "to bother to do ～ (although it's not necessary); to take the trouble to do ～; all the way; specially", whereas わざと means "do ～ on purpose (knowing it's usually a bad thing to do it); intentionally for a reason". But わざわざ sometimes means "intentionally", and in this case the two are interchangeable (e.g. "わざわざ/わざと聞こえるように悪口を言う").
In archaic Japanese, according to a 古語辞典 and this article, わざと meant something closer to わざわざ in the sense of "to bother to do ～". This sense of わざと is obsolete now. However the word わざわざ(し) also existed in archaic Japanese and it meant "contrived; artificial". I could not find the direct source that describes when and how わざわざ was coined, but they are probably not in a simple "original-derived" relationship as you might expect. Both existed, but there was a large shift in meaning.