The present paper provides a representation result for monetary risk measures (i.e., monotone translation invariant functionals) satisfying a weak maxitivity property. This result can be understood as a functional analytic generalization of Gärtner-Ellis large deviations theorem. In contrast to the classical Gärtner-Ellis theorem, the rate function is computed on an arbitrary set of continuous real-valued functions rather than the dual space. As an application of the main result, we establish a large deviation result for sequences of sublinear expectations on regular Hausdorff topological spaces.