I’d like to know too.
I know that Egyptian and subsequent Greek ideas involved the heart as the seat of intelligence ... so it would make sense that if you want to be aware of, or pay attention to, something you’d devote a little bit of your mind (located in your heart) to that thing - so ‘(focus a) small (bit of your) heart’ would make sense.
But I have no idea what Classical Chinese thinking was about where the seat of the mind would be.
The classical Chinese also saw the heart as the seat of the mind! I don't really know the origin of this phrase, but I imagine the meaning might be better understood as "be timid." Imagine being scared and timid and curling up (trying to make yourself smaller). I think the phrase "be careful" has something of that mindset.