I am a non-psychologist reading some papers from psychology. I keep seeing the term "norming experiment" (e.g. "Normative Representation of Objects: Evidence for an Ecological Bias in Object Perception an d Memory" by Konkle and Oliva). What do psychologists or neuroscientists mean by a "norming experiment"? It seems like the idea is to see which presentations of a stimulus are preferred to others?
Yes, a norming experiment is an experiment looking to establish what (if any) is the perceptual norm for a given stimulus, i.e. the level of the stimulus that appears neutral. In the paper you referenced, the stimuli are the size(s) of various objects, and the subjects were instructed to pick for each object a size that appeared neither too big nor too small, thus psychologically "just right" or neutral.
More generally, quoting from another paper:
Many sensory dimensions are thought to be represented relative to a norm, which itself appears psychologically neutral or unbiased. In vision, classic examples of these norms include “white” in the perception of color, or “static” in the perception of motion. Norms have also been implicated in the representation of higher-level stimulus attributes. Thus current models of face perception assume that faces are represented by their “identity trajectories” relative to a prototype or average face [...]. Such diverse examples suggest that norms may in fact be central to most perceptual judgments.