You will have to decide what your own opinion is on this matter. My opinion is that Gene is weak. Gene is a follower consistently throughout the story and calling him a coward would probably not be too much of a stretch. As he considers whether or not to jump from the tree, his fear of the jump is overridden by his fear of what people will think if he does not. In particular, he fears what Finney will think of him. This reminds me of what I hear some parents say to their children when they have followed a friend in some particularly foolish way, which is, "If such and such told you to jump off a bridge, would you?" This is a situation in which Gene would have had to answered "Yes" to this question. Finney told him to jump from the tree, so he did.
Peer pressure. Everyone else is jumping, so Gene does too, much to Finny's encouraging and persuasion. Gene, at this point in the novel, is easily influenced, and in some respects is still "finding himself." I don't think it necessarily means he is weak, but rather, human. In the absence of Finny, Gene later finds himself and his own opinions and personality, and grows the backbone he so sorely needs in the beginning of this novel.