The answer at the moment seems to be a clear "maybe".
There is a Cochrane review of this very topic. Combination contraceptives: effects on weight.
A Cochrane review is a study where people collect a lot of other studies on the subject, determine whether the studies were well-designed, and, if they were, review those studies and draw a conclusion from that. These reviews get updated as new data becomes available. They are generally considered to be of high quality.
The Cochrane review includes a section titled "Plain language summary", which is very helpful for those not familiar with scientific studies - also the review is quite long, so it's good to have a summary of the important points. I'll include a summary here nonetheless.
In the Cochrane, the author looked at studies of women taking combination contraceptives for more than three months that included data on weight gain. The current conclusion of the review (last updated January 2014) is
Available evidence was insufficient to determine the effect of combination contraceptives on weight, but no large effect was evident. Trials to evaluate the link between combination contraceptives and weight change require a placebo or non-hormonal group to control for other factors, including changes in weight over time
This means that they found few studies that compared women taking combination contraceptives to women taking a placebo or nothing. This makes sense because contraception is usually taken for, well, contraception, and giving women a placebo instead is often unethical. Those four trials did not find a relationship between contraception use and weight gain. However, the four trials also only included five oral contraceptives and the skin patch, not a very wide variety of contraception.
Most other studies compared oral combination contraceptives with other oral combination contraceptives or other methods of birth control (like the vaginal ring).
Of the 79 weight change comparisons evaluating two combination contraceptives, seven showed a difference in the mean weight change or the proportion of women gaining or losing more than a set amount of weight. Even if no association existed between combination contraceptives and weight, one would expect several significant results (Type I errors) since numerous comparisons were made. Regardless of statistical significance, the clinical significance seems negligible.
Basically, this means that the weight gains in these studies were so low that if a causation existed between taking contraceptives and gaining weight, the studies should have shown a more severe effect than they did. And even if no association existed, they would have expected more false positives than what was found.
Unfortunately, ultimatively the quality of the available studies is just too low to give a definitive answer at the moment:
More than 25% of the trials had high risk of bias due to lack of blinding or incomplete outcome data (Figure 1). The majority of studies had unclear risk of bias due to missing information on randomization sequence generation or allocation concealment.
An interesting side note is that most studies only consider weight gain as anything over 2 kilograms or five pounds, which is a bit more than the weight gain described in the question.