na-adjective
deadly serious; deadly earnest
Emphasizes extreme seriousness, often with a nuance of being overly or comically earnest. Used for people, expressions, or attitudes.
彼は大真面目な顔で冗談を言った。
He told a joke with a dead serious face.
そんな大真面目に考えなくてもいいよ。
You don't have to think about it so deadly seriously.
真面目 means 'serious' or 'earnest' in a neutral sense, while 大真面目 intensifies it to 'deadly serious' or 'overly earnest'.
Compound of 大 (おお, 'big, great') + 真面目 (まじめ, 'serious, earnest'). The prefix 大 intensifies the meaning.