Based on the analysis of the binding energy in light nuclei near the neutron drip line, the nuclei 6He,11Li ,14Be and 17B are considered as core-neutron-neutron three-body systems. The core-neutron and neutron-neutron interactions are assumed to be the weakly attractive exponential potentials. It has been shown that the three-body system can have a bound state even if any two constituents of the system cannot have a bound state. The anomalously large root-mean-square radii of 6He,11Li,14Be and 17B is due to the weak binding of the outer neutrons.