Try to match your popsicle sticks lengths, eliminate those with warps, cracks, etc.
Assuming there will be some sort of board supporting the weight on the top, make absolutely sure each corner of your structure is the exact same height so that no one corner is supporting more load than another.
Also, google Odyssey of the Mind, they have a similar competition with balsa wood, the structures hold an incredible amount of weight, see the link below.
http://www.odysseyofthemind.com/wf20.../bdsc_0141.jpg