Ahh I was looking for sentences where "すこしくらい" would work naturally. But I guess it doesn't here ><.
I was modifying a practice question, but now that I translate what I typed into English, it does seem a little strange too.. Still, I think I'm trying to mean say.. "That's quite a lot of luggage. Why don't I help you with some of it?"
１）荷物がたくさんあるので、 すこし運びましょうか？ or すこし手伝いましょうか？ or すこし運ぶの手伝いましょうか？
2)荷物がたくさんあるので、すこしくらい運びましょうか？ The latter 2) sentence usually implies that you guess the person would be unwilling to ask you to do it, ( because she/he thinks it would bother you or simply does't want you to touch the luggage or such) and you try to imply you understand what she thinks.