Ayaさんの英文で、I want to see him happy.
と I want to see him be happy. は良いですが、I want to see him being happy. とは言いません。
この場合、私なら次のように言います。
ーI'd like to see him be happy.
ご参考まで!
ご質問ありがとうございます。
・「I want to see him happy.」
「I wanna see him happy.」
=彼の喜ぶ姿が見たい。
(例文)Why did you buy that?// I got him this because I want to see him happy.
(訳)なんでそれ買ったの?//彼の喜ぶ姿が見たいからこれを買ってあげた。
お役に立てれば嬉しいです。
Coco