For a kinetic binding assay using Surface Plasmon Resonance or Biolayer Interferometry, how do I chose which of my binding partners to immobilize?

The relative size of the molecules isn't generally the deciding factor. Large proteins will typically give larger signals, but that isn’t necessarily better.

For protein/protein interactions, start by considering other properties of the proteins. Most importantly stoichiometry of binding. If one of the molecules is multivalent (an antibody, for example), then you should always try to immobilize it, as the fitting (to a 1:1 model) is much more straightforward. If both molecules are multivalent, try to immobilize at a very low density. If necessary you can fit to a bivalent analyte model. Other considerations are solubility and existing tags for immobilization.

For protein/small molecule interactions, you will typically immobilize the protein, as immobilization of small molecules is often difficult and or disruptive to binding. For small molecule interactions, a very stable capture method (e.g. biotin-capture) is recommended.