Keep in mind that stiffness is the cube of thickness. So if you double the width of a frame it is 8 times stiffer, and 4 times stronger in plane with the canvas. If you double the thickness (front to back) it is twice as stiff, and twice as strong. You don't want to get the stretcher parts too thin as you have to deal with wracking also.
So moving from the 2 x 3 to 3 x 3, you get 50% more strength and stiffness in the plane of the canvas. If you had made that member 2 x 4.5 same weigh and cost increase, you would increase stiffness on the plane of the canvas, 337%. Not to say one should have done that, but it is worth keeping in mind. If you increased dimensions 25% in both directions for 2.5 x 3.75 you would increase stiffness in both planes about 250%.
I should say that increasing thickness 50% (2 x 3 to 3 x 3), has a huge effect on stiffness out of plane with the canvas, if that is where you want it.