Rotations of asteroids have been set and altered by several processes since their formation. In the case of the near-Earth objects (NEOs), the rotational states are significantly affected by non-gravitational effects. In addition, an abundant population of binary systems has been found among NEOs with rotational periods very close to the spin barrier and in the size range from 0.2 to 10 km. In this paper we report photometric observations of about 80 NEAs carried out with the 1-m telescope of the Observatório Astronômico do Sertão de Itaparica (OASI, Brazil) from 2016 October to 2020 December. Reliable rotational periods and lightcurve amplitudes were determined for 46 objects, of which 15 are Potentially Hazardous Asteroids (PHAs). A minimum period value was also derived for other 11 NEOs. Then, asteroids with rotation periods between 2 and 3 h had their lightcurves analyzed for binarity signatures. We analyzed 21 binary candidates and for 8 of them we found the signature of a possible satellite. These suspected binaries showed a single possible mutual event or a secondary period superimposed on the lightcurve. Primary lightcurves for 6 confirmed binary NEOs were also obtained and for some of them the orbital period was also determined. Finally, we show that binary candidates require some internal cohesion strength to avoid structural failure by centrifugal forces.