Body mass (BM) and resting metabolic rates (RMR) are two inexorably linked traits strongly related to mammalian life histories. Yet, there have been no studies attempting to estimate heritable variation and covariation of BM and RMR in natural populations. We used a marker-based approach to construct a pedigree and then the ‘animal model’ to estimate narrow sense heritability (h^2) of these traits in a free-living population of weasels Mustela nivalis – a small carnivore characterised by a wide range of BM and extremely high RMR. The most important factors affecting BM of weasels were sex and habitat type, whereas RMR was significantly affected only by seasonal variation of this trait. All environmental factors had only small effect on estimates of additive genetic variance of both BM and RMR. The amount of additive genetic variance associated with BM and estimates of heritability were high and significant in males (h^2 = 0.61), but low and not significant in females (h^2 = 0.32), probably due to small sample size for the latter sex. The results from the two-trait model revealed significant phenotypic (r_P = 0.62) and genetic correlation (r_A = 0.89) between BM and whole body RMR. The estimate of heritability of whole body RMR (0.54) and body mass corrected RMR (0.45) were lower than estimates of heritability for BM. Both phenotypic and genetic correlations between body mass corrected RMR and BM had negative signals (r_P = -0.42 and r_A = -0.58). Our results indicate that total energy expenditures of individuals can quickly evolve through concerted changes in BM and RMR.