A fairly good sized change in barometric pressure is equivalent to a change in depth of about a foot and a half of water. It seems like most fish change the depth they are at a lot more than a foot and a half, a lot quicker than even the most rapid change in the weather can occur. So the effect on fish of an atmospheric pressure change alone, without regard to associated affects like temperature, precipitation, and sunlight vs. clouds, would seem to be pretty small.