That big brother is really watching out for his little sister.
That older brother is really careful about his baby sister.
この場合、次のような言い方ができますよ。
ーThat big brother is really watching out for his little sister.
「お兄ちゃんは妹をすごく気遣っている」
ーThat older brother is really careful about his baby sister.
「お兄ちゃんは妹をすごく気遣っている」
ここの「気遣う」は to watch out for ... や to be careful about ... を使って言うと良いでしょう。
ご参考まで!