Honestly Weeks is the unluckiest guy on the face of the earth. His career BABIP is like .280 even though his career LD% is around 19% (indicating an expected BABIP of around .310).
This year, though, he's been legitimately bad as a hitter, getting only 11% line drives and as a result a BABIP of only around .220. He has a good eye, as evidenced by his 29 walks in 213 at-bats, but he has also K'ed roughly 25% of the time. It's funny, b/c there are a lot of guys who can strike out 1/4 of the time and still put up a batting average in the 270-280 range (take a look at Alex Gordon this season). For some reason, Weeks is just a horrible hitter for average.
If you watch him, he doesn't have a level swing. It's very upper-cutty, very much like Gary Sheffield's swing. Unfortunately for Weeks, he doesn't have Sheffield's otherworldly talent for actually getting the bat on the ball...so when he hits it, he crushes it, but that's not very often.