Thermodynamics of a small sessile droplet on a solid substrate is discussed with a focus on size-dependence of its contact angle. An interface displacement (ID) model is employed to calculate profiles and contact angles of sessile droplets representing, in particular, critical droplets in nucleation on a partially wettable solid substrate. Line-tension and adsorption-related corrections to the contact angle cosine are found within the ID model and illustrated with numeric calculations for a short-range interface potential. The line tension and adsorption effects on the contact angle are shown to be comparable even in the first order in the contact line curvature. For smaller droplets, an intrinsic dependence of the line tension on the contact line curvature also becomes significant for the contact angle.