Scanning force microscopy (SFM) is used to investigate novel perturbation/response phenomena in a soft polymer network. Topics addressed include (i) the volume of film affected by tip-sample contact and (ii) the time-evolving residual signature of this contact. An outward deformation of nanometer-scale, soft, hydrated gelatin films is induced by the close proximity of the SFM tip. A domelike defect is created, centered at the site of approach and exceeding the tip-sample contact zone in diameter by as much as 3 orders of magnitude. The stretching of the film changes the stiffness of the polymer network and its frictional character. A precise correspondence of height and frictional force is quantified in histograms of the number of image pixels versus height or frictional force, and as a function of lateral distance from the center of approach. Relaxation of the dome is observed on a time scale of minutes with stretched exponential time dependence, consistent with a distribution of relaxation times. Film age also affects the size of the doming region : an increase to a maximum volume is observed followed by a decrease to nanometer scale dimensions with age. This apparently reflects competing increases of long and short-range order that determine film cohesion. Five stages of gelatin film aggregation are experimentally distinguishable, differing in the extent of cohesion generated by progressive intermolecular coordination (e.g., crystallinity).