The osmotic pressure of uncharged and weakly charged spherical oil-in-water microemulsion droplets was measured as a function of the droplet volume fraction, phi, in the concentration range 0.061 less than or equal to phi less than or equal to 0.44. The data from the uncharged droplets were analyzed in terms of a hard-sphere repulsion in combination with a van der Waals attraction. The droplet size, as obtained from the analysis, shows a good agreement with previously published small-angle neutron and light scattering data. The droplets were made weakly charged by replacing a small fraction (0.01, 0.04, and 0.06) of the nonionic surfactant with ionic surfactant, retaining the droplet size. The introduction of long-range electrostatic interactions resulted in a strong increase of the osmotic pressure. From comparison with model calculations, solving the Poisson-Boltzmann equation in the cell model, it is concluded that essentially all the ionic surfactant adsorbs to the droplets for phi > 0.1. At lower phi, however, the fraction of nonadsorbed ionic surfactant in the aqueous solvent becomes significant and increases with dilution. The degree of adsorption was also calculated within a molecular model, and a good agreement with the values obtained from the osmotic pressure data was found. When adding a large amount of salt to the charged droplets, the relevant osmotic pressure drops back to its original value for the uncharged case, demonstrating that the only influence of the ionic surfactant is the long-range electrostatic interaction.