Verified answer

It means "seeing/looking at ME." The words "a mí" add the emphasis.

"Seeing ME, (out of all people)!" The repetition gives emphasis, which in a Germanic languages like English we do by just shouting louder. Compare the French, which is a Romance language like Spanish, "en me voyant, â moi."

looking at me

Yeah it's "looking at me"

viéndome a mí = looking at me

http://www.spanishdict.com/translate/viendome%20a%...

My Viennese amphitheatre.