  In the context of the coloured stochastic vertex model in a quadrant, we
identify a family of observables whose averages are given by explicit contour
integrals. The observables are certain linear combinations of $q$-moments of
the coloured height functions of the model. In a polymer limit, this yields
integral representations for moments of partition functions of strict-weak,
semi-discrete Brownian, and continuum Brownian polymers with varying beginning
and ending points of the polymers.
