Research into haptic perception typically concentrates on mechanoreceptors and their supporting neuronal processes. This focus risks ignoring crucial aspects of active perception. For instance, bodily movements influence the information available to mechanoreceptors, entailing that movement facilitates haptic perception. Effortful manual wielding of an object prompts feedback loops at multiple spatio-temporal scales, rippling outwards from the wielding hand to the feet, maintaining an upright posture and interweaving to produce a nonlinear web of fluctuations throughout the body. Here, we investigated whether and how this bodywide nonlinearity engenders a flow of multifractal fluctuations that could support perception of object properties via dynamic touch. Blindfolded participants manually wielded weighted dowels and reported judgements of heaviness and length. Mechanical fluctuations on the anatomical sleeves (i.e. peripheries of the body), from hand to the upper body, as well as to the postural centre of pressure, showed evidence of multifractality arising from nonlinear temporal correlations across scales. The modelling of impulse–response functions obtained from vector autoregressive analysis revealed that distinct sets of pairwise exchanges of multifractal fluctuations entailed accuracy in heaviness and length judgements. These results suggest that the accuracy of perception via dynamic touch hinges on specific flowing patterns of multifractal fluctuations that people wear on their anatomical sleeves.