One thing that happened over the summer, I grew.

Grim takes a look at me one day and he goes, "all that walking you do, it must be stretching your legs, and carrying poor Kevin around that seems to be putting real muscle on you."

He's not that heavy, and anyhow it's not fair everybody always says, "poor Kevin", just because he didn't grow."

Grim gives me this long sorrowful look and then he clears his throat and says, "you're quite right, he is a rather remarkable boy".

He memorized almost the whole dictionary, you can ask him anything, and he knows what it means!

"You don't say", Grim says and he has this smug look like maybe Freak is lying and a total goon like me would never get it, and I want to tell him he's wrong about Freak and the dictionary, but instead, I just shut my face and go down under.

Put a colon after "grew" in the first one.

In all the others, be sure to start each quoted section with a capital letter.

There's a run-on in the third one.
http://grammar.ccc.commnet.edu/grammar/runons.htm

Comma after "look" in the fourth one. Also there's a run-on in the quoted section in the fourth one.

Run-on in the fifth one.

The sixth one needs to be divided into three sentences -- not so many clauses strung together with commas.