I am exploring the phonological system of Kyrgyz Language.
In casual speech people tend to change b > w when b occurs between two vowels or preceeds l, r, y and followed by vowel. Are there other languages where b changed into w? What may be the reasons for it?
This is a common process called lenition.
Consider a language that has a phoneme /b/ as its only voiced bilabial phoneme. Speakers will then often pronounce /b/ without complete closure of the airway, giving a fricative [β] or approximant [β̞] realization.
A very similar phenomenon occurs in Spanish, Portuguese, and Catalan, where intervocalic /b/ is realized as [β̞]. For example, Spanish bobo /ˈbo.bo/ will be pronounced [ˈbo.β̞o]. Japanese similarly often realizes /b/ as /β/.
In this case, the (voiced bilabial) stop turns into an approximant. Kyrgyz lacks a /w/ phoneme, so there is no need to distinguish /b/ from /w/. Since the bilabial approximant [β̞] sounds similar to the bilabial-velar approximant [w], it is not surprising that [w] is another possible realization. Such shifting between various labial sounds and [w] is very common cross-linguistically; examples include:
Another such transformation is Ancient Greek βῆτα [bɛ́ɛ̀.ta] 'the letter beta' -> Modern Greek Βήτα [ˈvi.ta], where the /b/ was lenited to /β/, which was replaced with the cross-linguistically-more-common labiodental phone.
