I am not Hyde, but gaining weight (both muscle and fat) can help all three lifts progress to a point.
For bench, this is because your become thicker so the bar may travel less distance. As your tissues (both muscle and fat) around the elbow and lats increase, this can create a tissue on tissue compression helping to move the load out of the bottom. Another factor is that you are now heavier, so your center of gravity is altered in relation to the load on the bar, this can help with bar control and stability. It is common to see heavier guys with a more flat back approach and legs out front, you would think a less condensed, tight, and arched set up would result in less weight being moved, but it is not usually the case due to them being heavier. On the flip side, smaller guys tend to lean towards feet back and arching to condense their weight and provide more stability and bar control.
For squat, the same tissue and on tissue effects can happen with the knees and stomach into the thighs. Also a thicket waist can provide a lower center of gravity giving more bar control and overall stability to the load on the shoulders and during the squat.
For the deadlift, the same tissue on tissue effect can happen as well with the stomach into the thighs, but if this is pushed to the point where now the bar is out in front of you to work around your bigger size, the leverage you once had is decreased thus making the lift harder. This is usually the inflection point where gaining weight can make one's deadlifts worse, when it impacts your starting position negatively. In theory, gaining way too much weight can negatively impact all three lifts, but the margin for this tends to be much lower on deadlifts to where one could be gaining and still getting stronger as a result of that on bench and squat but their deadlift can start to be impacted negatively.