Actually, it's opposite. For two sticks with the same weight, the stick with the bigger cross-section area is going to be the strongest under a compressive load. It's all in the Euler Critical Buckling Load Equation. So a 1/8" x 1/8" stick that weight the same as a 3/16" x 3/16" stick is going to be weaker, not stronger.
Now, if you have two sticks with the same density, the stick with the larger cross section will be stronger, but also weigh more and therefore may or may not be less efficient than the stick with the smaller cross section.
Essentially, Euler's Critial Buckling Load Equation says that the maximum load (critical load) you can apply compressively to a column (stick) is inversely proportional to the length of that column (stick) squared and directly proportional to the cross sectional area squared. So if you have square sticks, the critical (max) load you can apply is directly proportional to the side length to the fourth power! On the other hand, Euler's equation says the critical (max) load is only directly proportional to the Modulus of Elasticity (MOE) to the first power. Typically the MOE increases linearly with density, so essentially you can say that the critical (max) load is only directly proportionally to the density to the first power and directly proportional to the side length to the fourth power.
That is why it is usually advantageous to increase the cross-sectional area of your stick, while keeping the same density as the thinner stick, in order to increase the maximum compressive load that the stick can handle before buckling (failing). Increasing the density, while keeping the stick thickness the same, does increase the strength, but you get more bang for your buck by increasing thickness rather than density. This is an important principle and is kind of one of the main things we hope students will learn from this event.
Hope this helps.
