just think of it at the extremes and the principles become pretty clear.
"strength is gained by larger diameter"
-imagine a piece of .5 inch diameter .120 wall tubing. you could probably bend it by hand. now imagine a 3 inch diameter .120 wall piece. there is NO way you're gonna bend that by hand. the wall thickness stayed the same, the diameter increased, so did the strength.
"strength is lost by thinner wall"
-imagine a piece of 1" diameter .25 wall. you could NOT bend that by hand. now imagine a piece of 1" diameter .01 wall, paper thin tubing. you could bend it by hand. the diameter stayed the same, the wall got thinner, the strength was decreased.
that covers bending forces.
for tension, it is a function of the cross-sectional area of the steel. a larger diameter will increase the cross-sectional area, and a thinner wall will decrease the cross-sectional area.
Since both diameter and wall thickness influence strength there is a balance to be acheived. You'd have to get someone with the engineering books to figure out where that balance lies exactly.