This one took me some time. Here's my reasoning.
The argument is that the increasing popularity of soccer is causing people to lose interest in baseball, and therefore, the attendance at baseball games is decreasing.
Now, we have to find something that weakens the above, meaning something that would say that the popularity of soccer has no effect on the attendance of baseball game audience.
(A) The publisher of the Constitution-Herald is an avid baseball fan. - Irrelevant. Him alone cannot be any counting factor.
(B) All baseball teams in the country are showing reduced attendance due to the growing popularity of soccer. - Strengthens.
(C) The owner of the local baseball franchise also owns the soccer franchise. - Irrelevant. How does it affect the audience?
(D) Nearly all local fans who go to baseball games read the sports coverage only in the local paper Sport City, which has not changed its coverage of baseball. - CORRECT. Fans of baseball are still reading about it in the paper. The less coverage in the Constitution-Herald does not signal that the fans of the game has stopped reading about it or are losing interest in it.
(E) In general, newspaper readers prefer to watch basketball. - Irrelevant. We are not discussing basketball at all.