The static reconfiguration of a weighted flexible ribbon of trapezoidal shape, exposed to fluid flow, was investigated by means of highly resolved numerical simulations, configured to match the experiment of Barois and de Langre [J. Fluid Mech. 735, R2, 2013]. Over a broad velocity range, the ribbon experiences a drag force nearly independent of the flow velocity. This phenomenon is regarded as a unique characteristic of tension-controlled reconfiguration, in contrast to the more prevalent case of elastic reconfiguration in literature. The present paper provides a detailed analysis of the flow field in general and the interaction with the ribbon in particular, for example in terms of distributed fluid loads acting on the ribbon. Situations with small and strong reconfiguration of the ribbon reveal fundamentally different wake regimes, hence strongly influencing the characteristics of fluid loading. The findings enabled to develop an enhanced theoretical model in a self-similar framework, especially including a physically justified, realistic local drag coefficient, termed streamline-based local drag model (SLDM). The modeling approach provides an even deeper understanding of the mechanisms during reconfiguration.