We studied a sample of 27 T Tauri stars (TTs) showing a weak Ha line, selected from the Pico dos Dias Survey, a search for young stellar objects. A model to fit the spectral energy distribution is used in order to reproduce their observed infrared excess and to evaluate the individual contribution of the circumstellar components (dust disc and/or envelope) to the total emitted flux. The objects were separated into different categories of young stars, searching for an agreement with an evolutionary sequence. The classification is based on the stellar characteristics as spectral type; equivalent width of the Li 670.8-nm line; optical and X-ray properties; and infrared excess. We conclude that only 41 per cent of our sample actually correspond to weak TTs, and the remaining objects are mainly classical TTs or young main-sequence stars. Most of the stars have a near-infrared index typical of Class II objects and show an important fraction of the observed emission (∼30 per cent) being generated by the circumstellar material.