As individuals age, there is a tendency to gain weight, with or without BCPs.
It is difficult to show any significant additional weight gain in groups of women taking low-dose BCPs compared to groups of women (of the same age) not taking BCPs.
That said, there are certainly individual women who gain weight when they take BCPs and lose the weight when they stop taking the BCPs. Similarly, there are individual women who lose weight while taking the BCPs and gain it back when they stop.
For those women who tend to retain water in the presence of elevated estrogen levels, changing them to a stronger progestin pill with a longer half life may resolve the weight gain problem. This works because the stronger progestin will more consistently suppress ovarian function, suppressing the woman’s own estrogen, while providing a small amount of “add-back” estrogen from the pill to prevent such hypoestrogenic symptoms as night sweats, vaginal dryness, and hot flashes.
For the same reason, some women during the first month of BCPs will notice fluid retention and associated weight gain due to the elevated hormone levels. After the first month, when ovarian suppression sets in, the hormone levels drop to normal or slightly below normal, and the fluid retention resolves. Unless the particular pill is not strong enough to suppress ovarian function. In those cases, the fluid retention will continue until the pill is switched to a variety that will consistently suppress the ovaries.