We present a micromagnetic theory of compact magnetic skyrmions under applied magnetic field that accounts for the full dipolar energy and the interfacial Dzyaloshinskii-Moryia interaction (DMI) in the thin-film regime. Asymptotic analysis is used to derive analytical formulas for the parametric dependence of the skyrmion size and rotation angle, as well as the energy barriers for collapse and bursting, two processes that lead to a finite skyrmion lifetime. We demonstrate the existence of a regime at low DMI, in which the skyrmion is stabilized by a combination of nonlocal dipolar interaction and a magnetic field applied parallel to its core, and discuss the conditions for an experimental realization of such field-stabilized skyrmions.