This is just basic physics, OP.
you have a spec of fret buzz (must have a nice low action... or really bad fret work, probably just low action though).
So when you play lightly, you are just stopping the string at the fret, making a line from string raise at the nut down to the fret lower than your finger (in pitch), straight across under your finger (you're not pressing hard so not bending the string down toward the fingerboard between the frets), and then the string gradually rises from the upper fret (the pitch fret) to the bridge saddle.
Now, what happens to any bass string when you press it harder? You BEND the string, between the lower and upper frets (so only like an inch or so of string length is being bent between those two firm points).
And what happens to the string on either side of the frets? The string, VERY SLIGHTLY, follows the path of the bend that you created. So you push the string down, bending it into the instrument, and on the other side of the fret, very very slightly (only very slightly because of string tension that is trying to straighten the string constantly).... very very slightly bends UPWARDS, away from the instrument. Just a few microns or whatever, but enough that the string is now very slightly higher over the first non-pressed fret.... thereby reducing string buzz.
I am making some educated guesses here about the tension of the string versus the string's desire to not be bent... but I'm fairly sure that this is what's going on. I've experienced it my whole life, also on guitar, and I use that knowledge to my benefit for different types of playing (very very cleanly, for example, when recording)... although on guitar if you're a serious guitarist you also press certain notes harder than others to fine tune chords for the best interval tuning... and you learn early on that it also reduces string buzz on the string you press harder (only).