To be honest, both parties are in the wrong. Drake, for taking money from Meek to write a verse in the song they collaborated in, but then getting someone else to write it. Meek, for airing him out on Twitter when he could have confronted him like a man about it, face to face. No one has face-to-face confrontations in hip hop anymore, save for the time Diddy got physical with Drake and the time Trae tha Truth broke Mike Jones' nose. Even Jay-Z himself doesn't confront anyone, but he'll mention your name in a song, though. LOL.
Other than that, the reason for the beef between Drake and Meek is really very petty. Both diss songs were average at best, too. The reaction I had for both of them doesn't even compare to the reaction I had for Ether, Takeover, Curtis, Piggy Bank, Back Down, Checkmate, T.I.'s entire Down with the King mixtape, etc.
Oh, and @dccomicsrule2011, agreed on the Hit 'Em Up being the most overrated diss song ever. Pac was beefing with himself with that one.