You're better off keeping your luggage to a minimum. I don't need anything but I appreciate the offer.
You should travel as light as possible! Don't worry about bringing anything for me. I appreciate the offer though.
「荷物は少ないほうがいいんじゃない？気持ちだけで大丈夫です、ありがとう」＝ You're better off keeping your luggage to a minimum. I don't need anything but I appreciate the offer. / You should travel as light as possible! Don't worry about bringing anything for me. I appreciate the offer though.
ボキャブラリー
be better off ＝ ～をした方がいい
luggage ＝ 荷物
minimum ＝ 出来るだけ少なく、最低限
appreciate ＝ 感謝する、ありがたい
travel light ＝ （旅行の時）荷物を少なくする
don't worry ＝ 気にしないで
この場合、次のような言い方ができますよ。
ーIt's better not to travel with too many things.
「多くの物と旅行をしない方が良い」＝「荷物は少なめで旅行した方がいい」
ーTravelling lightly is the way to go.
「身軽で旅をするのがよい」＝「荷物は少なめで旅行した方がいい」
ご参考まで！
イギリス 
カナダ 
