Variant pronunciation of "obesity"
The OED says of that word’s pronunciation:
obesity /əʊˈbiːsɪtɪ/, older /-ˈbɛsɪtɪ/.
That says it used to be pronounced with an /ɛ/ instead of the /i/ that is universally heard today.
Also, the first vowel in General American is more likely to be [oʊ] than the RP [əʊ] vowel which does not occur in GA. However, since it is not stressed, it is subject to typical reduction patterns, which can lead to [o], [ɒ], [ɵ], or [ə] in rapid or relaxed speech.