first things first.
The graph is a histogram of the form 1/x^2
No, the graph has the form e^(-BE), as you stated in the first paragraph.
To understand why the graph for molecule velocity distribution first rises and the falls, you must realise that this distribution takes two factors into consideration. The number of molecules with a given velocity is the product of the probability of a molecule being in a given state with that velocity (that's the one that goes like e^(-BE)) multiplyed by the number of states possible with that exact velocity. That second factor grows, and the product of the two first go up and then comes down.
Edited by fallacycop, : Typos
™ Version 4.2