HL's Independence- or lack thereof...

Posting about AW's independence got me thinking about HL's lack of the same... HL often resists independence to the point of driving his parents mad. He knows and we know that he can things on his own, but he will just downright refuse most of the time. Extremely frustrating, I tell you. I suspect that a portion of his attitude has to do with having a little brother who needs/ed help continuously- HL sees AW getting all this attention needing help, so he tries to put himself in the same situation. Our response has been something to the effect of "you can do it yourself now, or wait patiently until I am ready to help you." Unfortunately, he often ends up in trouble for not being patient, causing the situation to quickly deteriorate. Even his teacher is noticing this behavior and mentioned it at our parent-teacher conference. I hope that AW's new self-sufficiency will prompt HL to do the same, because I am truly getting frustrated by his behavior and am searching for a solution...