Early elementary schoolers might compare their results to peers, or be challenged to try and beat the day's "top bridge design" (e.g. the design that held the most amount of weight so far that day).
Children at this age can compare the overall amount of weight held by two different bridges using a balance scale (e.g., by putting all of the weight held by one bridge on one side of the scale, and all of the weight held by a second bridge on the other side of the balance scale).
Some children this age may want to work together to build a bridge. Teamwork is strongly encouraged for any engineering task and is a valuable skill for children to practice (real-world engineers often work in teams!).
Early elementary schoolers can attempt to guess how many weights their bridge will hold, and why some bridge designs work better than others.
They can also hypothesize which of two bridges they think will be the "best design" (which will hold the most weight) and then test their ideas with an experiment.
Early elementary schoolers can see connections between the design of their paper bridge and the results they get when they test it.
They can also observe why their less successful bridges might have failed, and how they might be able to prevent those bridges from collapsing in the future.
Early elementary schoolers can attempt to create their own paper bridge without looking at previously created example. Before children at this age get to designing or testing a bridge, grownups can encourage them to brainstorm about bridges. Looking at examples of real or model bridges (in pictures, with 3-dimensional models, or outdoor bridges) will help children at this age come up with their own designs.
Early elementary schoolers are developing an understanding of the importance of working with a limited amount of materials to solve problems. Encourage children at this age to think about how a real engineer would build a big, strong bridge with only (for example) a few beams and bolts, or a pile of wet concrete, without running out of supplies? Grownups can "increase the design constraints" for paper bridges, by challenging children to build a bridge using only one piece of paper.
Early elementary aged children are adept at using scissors and carefully balancing objects. They have the fine motor skills to fold and roll paper in a variety of shapes and to stack objects on their bridge, without knocking it over.
Children this age can also make comparisons between different kinds of objects- if you use two different types of "weights" to test the bridges, children this age can be encouraged to try and figure out, for example, how many plastic chips weigh as much as a single plastic turtle.