  We prove tightness and limiting Brownian-Gibbs description for line ensembles
of non-colliding Brownian bridges above a hard wall, which are subject to
geometrically growing self-potentials of tilted area type. Statistical
properties of the resulting ensemble are very different from that of
non-colliding Brownian bridges without self-potentials. The model itself was
introduced in order to mimic level lines of (2+1)-dimensional discrete
Solid-On-Solid
  random interfaces above a hard wall.
