Translation:He is big, even though he eats vegetables.
I think this is another case of needing separate definitions for "alors" and "alors que."
Is there a lesson later on for idiomatic expressions that don't have very good literal translations? Maybe there should be one earlier on for phrases like "alors que" and "depuis que" to show how words like "alors" and "depuis" can take on slightly different meanings in different contexts/when combined with different words...?
Actually, "even though" was listed first on Duo's drop-down hints for "alors que". And despite the testimony to the contrary, one translation of "alors que" is "even though" which makes perfect sense in this sentence. http://www.larousse.com/en/dictionaries/french-english/alors/2490#2491