The phrase "at advantage" is spelled with three syllables: /æt/ /ədˈvæn.tɪdʒ/. The stress is on the second syllable, "van." The "a" in "at" is pronounced as the short "a" sound, and the "t" is pronounced without any aspiration. The "v" in "advantage" is pronounced as a voiced labiodental fricative, while the "n" is pronounced as a voiced alveolar nasal. The final "ge" is pronounced with a soft "j" sound followed by an unstressed /ə/.
The phrase "at advantage" actually does not have an etymology of its own. Instead, it is a combination of the preposition "at" and the noun "advantage".
The word "at" comes from the Old English word "æt" and has had a consistent usage and meaning throughout its history.
On the other hand, "advantage" has a more complex etymology. It originated from the Latin word "ad- (to, toward)" and "vantage (profit, gain)". In Middle English, it was spelled as "avauntage" and gradually evolved to its present form.
When these two words are combined, "at advantage" means being in a situation where one has a favorable position or superior condition.