Carboxysomes are self-assembled bacterial microcompartments that facilitate carbon assimilation by colocalizing the enzymes of CO2 fixation within a protein shell. These microcompartments can be highly heterogeneous in their composition and filling, so measuring the mass and loading of an individual carboxysome would allow for better characterization of its assembly and function. To enable detailed and extended characterizations of single nanoparticles in solution, we recently demonstrated an improved interferometric scattering anti-Brownian electrokinetic (ISABEL) trap, which tracks the position of a single nanoparticle via its scattering of a near-infrared beam and applies feedback to counteract its Brownian motion. Importantly, the scattering signal can be related to the mass of nanoscale proteinaceous objects, whose refractive indices are well-characterized. We calibrate single-particle scattering cross-section measurements in the ISABEL trap and determine individual carboxysome masses in the 50-400 MDa range by analyzing their scattering cross sections with a core-shell model. We further investigate carboxysome loading by combining mass measurements with simultaneous fluorescence reporting from labeled internal components. This method may be extended to other biological objects, such as viruses or extracellular vesicles, and can be combined with orthogonal fluorescence reporters to achieve precise physical and chemical characterization of individual nanoscale biological objects.