You probably would need a moon
You apparently want to have a situation that would cause people on one side of your planet to feel less gravity than normal at specific times. This cannot be done with a flyby planet. The reason is that whatever gravitating mass there is pulls all the other masses towards itself, thus anything in the sky would pull both people and the planet, with force difference reversely proportional to cube of distance to that mass divided by planet radius. So, the Sun, even being quite heavy vs the Earth, does very minimal gravity difference on the surface, because it's very far. Thus, in order to have another celestial body to influence gravity on your planet, you need a moon.
The planet's moon
Imagine Earth having its Moon being about six times closer to Earth than it is in reality (9 radii of Earth, or 57330 km away from surface, on a circular orbit with radius of 10 radii of Earth, or 63700 km). This change would make people on the side that's facing the Moon to be pulled towards the Moon with acceleration of
6.67e-11*3.347e22/5.733e7^2 = 6.792e-4 m/s^2, but the Earth would be pulled towards the Moon with acceleration of 5.502e-4 m/s^2, making the difference of gravity to equal 1.29e-4 m/s^2. The Earth's gravity is 9.81 m/s^2, so even if the Moon would be at 10 Earth radii orbit, it would only make people on Earth lighter by 1.31e-5 fraction, or 1.31e-3 percent. This is way not enough to make people jump higher by a visible margin.
But actually, even with our Moon located at its original distance, there are quite a lot of effects from Moon's gravity influence. Tides, for example, are the most prominent, but there are also some effects against Earth's crust and mantle, which are of about the same magnitude (12 km of crust vs 6370 km of radius - too small difference to notice here). But with Moon placed this close, all the effects would be marginally stronger, about 200x stronger, mind you! (6^3=216) Thus, tides would on average be 14 times larger (sqrt(200)), any forces applied to crust will be 200x higher, this would make Earth a lot more inhospitable. If you would plan to have a planet fly by, the effects would be marginalized even more, to the extent of a high tide wave flooding cities or valleys - this would be more visible than "people can jump a bit higher".
The planet IS a moon
Another possibility is to make your planet a moon of some gas giant, which would be large enough to create such disturbances of gravity on the planet's surface. But then your planet has to be outside the gas giant's Roche limit (for the planet, this limit also depends on the planet's mass) in order for it to stay whole. There would be a lot of tidal effects on that planet from the gas giant's gravity, which will quickly make the planet tidally locked, aka facing the gas giant with one side. Provided you will find the exact numbers that would make the planet's orbital period be small enough to count as a "long day" and the giant to be located in the star's habitable zone, this configuration can possibly provide your people with "seasons", yet there will be two areas with lower gravity than on the rest of the planet, one directly under the gas giant and the other on the opposite side of the planet. You can still postulate that the planet still maintains relative spin to the gas giant, as if the tidal locking hadn't fully happened, creating your high jump seasons, but remember that there will be also high tides.