I haven't really gotten into Heaver Things, but to be fair, I haven't given it a fair chance. I love Room for Squares.
I have a lot of respect for him for a number of reasons: one, I think he's extremely articulate - when I've heard him speak or when I've read interviews, he's always saying really wise, accurate things that extend well beyond his years.
Two, he's an unbelievable guitarist.
Three, he's not afraid to stray from the three-minute pop song (even though many of the people in his audience are really there for the radio-friendly songs) and just jam.
Four, he's well aware of his influences, and while he emulates them, he's highly respectful of them. Did anybody see the Austin City Limits where Double Trouble backed him and he performed with Buddy Guy? Astounding that he even had the guts to play with them - and yet he was aware and cognizant of their greatness.
Five, he's not afraid to get ugly - really fucking ugly - with his guitar faces.