  We study a scaled version of a two-parameter Brownian penalization model
introduced by Roynette-Vallois-Yor in arXiv:math/0511102. The original model
penalizes Brownian motion with drift $h\in\mathbb{R}$ by the weight process
${\big(\exp(\nu S_t):t\geq 0\big)}$ where $\nu\in\mathbb{R}$ and
$\big(S_t:t\geq 0\big)$ is the running maximum of the Brownian motion. It was
shown there that the resulting penalized process exhibits three distinct phases
corresponding to different regions of the $(\nu,h)$-plane. In this paper, we
investigate the effect of penalizing the Brownian motion concurrently with
scaling and identify the limit process. This extends a result of Roynette-Yor
for the ${\nu<0,~h=0}$ case to the whole parameter plane and reveals two
additional "critical" phases occurring at the boundaries between the parameter
regions. One of these novel phases is Brownian motion conditioned to end at its
maximum, a process we call the Brownian ascent. We then relate the Brownian
ascent to some well-known Brownian path fragments and to a random scaling
transformation of Brownian motion recently studied by Rosenbaum-Yor.
