Probably from 又 (*wu), with an unknown suffix added.
吾里 (*WUli)
In Old Korean orthography, native terms with clear Chinese equivalents are usually written with an initial Chinese character (logogram) glossing the meaning of the word, followed by one or more Chinese characters (phonograms) that transcribe the final syllable or coda consonant of the term. In the case of 吾里, the first character shows that this is the native Old Korean word for “we; us”, and the subsequent character(s) show(s) that the final syllable of this word is *-li. Because the semantics and the final phoneme(s) match, the word is conventionally reconstructed as *WUli, the ancestor of Middle Korean 우리 (Yale: wuli). Note that the reconstruction was not necessarily the actual pronunciation. Rather, it should simply be considered as a method of representing an Old Korean form phonetically by using its Middle Korean reflex.
According to scholarly convention, the elements of the reconstruction which are not directly represented by phonograms are given in capital letters. This allows readers to identify what part of the reconstruction is attested and what part is applied retroactively from the Middle Korean reflex. Middle Korean merged Old Korean *r and *l unconditionally, and it is not easy to determine the Old Korean phoneme based on the Middle Korean reflex. Old Korean reconstructions are conventionally given in the Yale Romanization of Korean, which makes only those phonemic distinctions also made in Middle Korean. However, Alexander Vovin gives circumstantial evidence that the syllable being transcribed by 里 is *li with a lateral consonant.