I was gonna say that you could make some huge bridge that could hold up anything until I saw their creative scoring formula which determines your score based on the weight of your bridge.
I'm gonna say that since you can assume that any surface facing the table is also restrained, that an arch bridge is your definite best bet. Instead of just having 2 contact points with the table you can increase that to however many you want by using downward vertical supports on the end of the bridge that are restrained by the table. This is the traditional design that railroads have used for supporting massive loads at minimal cost (which would equate to weight in your test). But it will only work if the deck of the table is deep enough, otherwise the legs of your arches won't have a solid surface to push against.
If that might be bending the rules a bit, and you want to stick with something conventional and only 2 contact points with the table, I'd go with a Whipple truss design, also very popular with the railroads for high load capability.
