  Several recent works have considered the pressure exerted on a wall by a
model polymer. We extend this consideration to vesicles attached to a wall, and
hence include osmotic pressure. We do this by considering a two-dimensional
directed model, namely that of area-weighted Dyck paths.
  Not surprisingly, the pressure exerted by the vesicle on the wall depends on
the osmotic pressure inside, especially its sign. Here, we discuss the scaling
of this pressure in the different regimes, paying particular attention to the
crossover between positive and negative osmotic pressure. In our directed
model, there exists an underlying Airy function scaling form, from which we
extract the dependence of the bulk pressure on small osmotic pressures.
