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