Miniaturization of small metallic systems can lead to a softening of the mechanical behavior due to the reduction of scale. Size effects have been considerably studied recently for materials with various crystallographic structures. Under tensile conditions, thin specimen exhibit softer mechanical properties when the number of grains across thickness is lower than a critical number and this modification appears above a critical strain level. In this work, stamping tests were performed on five hundred micrometers in thickness sheets of hexagonal closed-packed cobalt. The results are compared with those obtained for face centered cubic copper and nickel. The influence of thickness over grain size ratio was studied for several proportional loadings linked to forming processes. Complex loadings were applied with 20 mm hemispherical punch and strain paths were checked with a 3D video extensometer. Hill criterion was systematically used to take into account the anisotropy of the samples. Our results revealed that the critical strain level for which the size effects appears is strongly sensitive to the stress triaxiality which, in turn, is closely dependent to the loading path.