Parameter fitting in metabolic models can be challenging because experimental data are often noisy and sparse. In Bayesian estimation, prior knowledge about model parameters would be weighted against knowledge from data fitting. Since error bars and prior widths are often unknown, we explore a more flexible way of regulating this trade-off. We propose an evolutionary multi-objective approach to parameter estimation to find compromises between parameters matching the prior (prior loss) and yielding good data fits (likelihood loss). Our metabolic model describes an ensemble of steady states with correlated variation of all model variables. In the estimation, reaction elasticities are the parameters and the covariances of measurable state variables serve as measurement data. To evaluate our approach, we conduct two tests with artificial data and a known ground truth. We first consider a simple metabolic pathway with 3 reactions and 4 metabolites, where the correlated variation of variables can be understood intuitively. The second test involves a more complex real-world metabolic model of Escherichia coli bacteria with 62 metabolites, 57 reactions, and 234 elasticity coefficients to be fitted, where the results are almost impossible to guess even for domain experts. In both cases, the proposed method yields satisfactory results. This paves the way to studying biological objective functions unrelated to model fitting, including homeostasis or information transmission across metabolic networks.