The experimental approach presented in this article investigates low-velocity small-diameter cylindrical viscoelastic jets. It consists in producing and analyzing sets of jet portion images taken at different positions along the jet axis, i.e., from the nozzle producing the jet down to the spray region. A very significant part of the work was dedicated to develop analyzing tools: a proper orthogonal decomposition to identify the onset of the capillary instability, a procedure to determine the mean jet breakup length and a multi-scale tool to describe the jet local shape and its evolution along the jet axis. Used in a similar previous study, the multi-scale analysis has been extended in the present work. These tools are shown to be well suited to the experimental study conducted here, and in particular to meet the need for statistical analysis that free jets impose. They are applied to study the capillary instability of free jets of dilute polyethylene oxide solutions produced from a micrometer nozzle. The parameters of the study are the molar mass of the polymer and the velocity of the jet. Results on the detection of the capillary instability onset, the jet evolution dynamics towards the Bead On A String (BOAS) pattern, the local extensional relaxation time and the terminal elongational viscosity of the solutions, the bead coalescence mechanism and its influence on the size of the spray drops are obtained. Analysis of these results reveals that the polymers undergo two episodes of mechanical degradation during the process: the first one at injection, the second one during the elasto-capillary regime of the jet breakup. Moreover, the scenario in the literature suggesting a sufficiently relaxed axial tension of the flow for the capillary instability to occur is found to be not always valid. It is also shown that the average size of the drops correlates with the intensity of the bead coalescence mechanism that takes place on the BOAS. These results demonstrate the richness of the adopted approach and in particular of the multi-scale analysis to study the development of a fluid interfacial instability.