Sorry for the brief answer yesterday, I typed a long post and it vapourized, then company showed up.... I'll try and get this done before family wakes up this morning....
Weight is very important in it's contribution to BC, but only because that it increases the Sectional Density of the pellet.... The SD is the "weight per unit area", so a 14 gr. pellet in .177 has a higher SD than in .22, and a 25 gr. in .22 cal. has a higher SD than in .25 etc.etc…. The other governing factor in the BC is the Form Factor, which is an indication of the "slipperiness" of a pellet.... The three are interrelated by the formula....
BC = SD / FF
and if you know any two, you can calculate the other one.... This is complicated because the FF is different if you use a different drag model (eg. G1 or GA) you get a different BC and FF, but let's not get sidetracked and assume we are using the GA model, which is the best we have at the moment for diabolo pellets....
When I joined the Hard Air Magazine "Team" as Technical Editor, I suggested that they add two more columns to the table of Ballistics Coefficients for the SD and FF, and they have done that.... As far as I know there is no other table for pellets that shows all three numbers, and not only that, but by clicking on the top of each column, you can sort the data by the values in that column....
https://hardairmagazine.com/ballistic-coefficients/For instance, if you sort by SD, within each caliber you will find that the pellets are then arranged by weight.... If you sort by FF, you will find that the round nosed pellets rise to the top (with bullet shapes above them, if any) while wadcutters end up at the bottom of the list.... This makes sense, because wadcutter have more drag.... Unfortunately, all the pellets are not tested at the same velocity (because they are tested in the same gun, only changing the barrel between calibers)…. Since the BC varies with velocity (and so does the FF), you can't make 100% accurate comparisions between calibers, but the imformation is still very valuable and enlightening....
Bottom line is that for a given shape of pellet (eg. the JSB EXact Series) the BC tends to follow the SD, regardless of caliber.... It's not a perfect correlation, because the velocities tested are not all the same.... and the shape does vary because of the weight changes, so the FF isn't always the same.... but you will notice that the JSBs tend to have the best FFs, which means they are one of the lowest drag pellets around.... In fact, when I am curious about what the BC may be of a new JSB Exact, I calculate the SD and divide by a FF of 1.5 to approximate the BC.... In many cases, it is pretty dang close....
The Wind drift is dependant on the Drag Coefficient and the velocity.... It is strictly related to the "lag time", which is the difference between the flight time of your pellet and what it would have been in a vacuum.... Even if the BC was a constant over the entire range of velocities, as I explained in the thread Alan linked above, the Cd is not, it has a huge increase in the Transonic range (Mach 0.8-1.2)…. This means that even though the flight time is shorter at high velocities, the lag time is greater, and so is the wind drift.... Here is a diagram showing what happens to the wind drift at different velocities....

and here is a more detailed example for a typical RN pellet at only 50 yds....

I hope this helps clarify things for you.... Yes, weight is important, but so is the shape and the velocity, in determining the wind drift.... All three factors interrelate, and not in a way you can easily calculate, because the drag (Cd) curve is different for each pellet, and basically none of them precisely match the GA model which programs like ChairGun use to calculate the trajectory and drift.... Still, at the present time, it is the best tool we have, and you can make two generalizations....
At a given velocity, a higher BC pellet will have less wind drift....
For a given BC and range, there will be an optimum MV where the drift will be at a minimum....
Bob