  We study the KPZ equation with a $1+1-$dimensional spacetime white noise,
started at equilibrium, and give a different proof of the main result of
\cite{bqs}, i.e., the variance of the solution at time $t$ is of order
$t^{2/3}$. Instead of using a discrete approximation through the exclusion
process and the second class particle, we utilize the connection to directed
polymers in a random environment. Along the way, we show the annealed density
of the stationary continuum directed polymer equals to the two-point covariance
function of the stationary stochastic Burgers equation, confirming the physics
prediction in \cite{MT}.
