The weak molecular attractions of nanoparticles are important because they drive self-assembly mechanisms, allow processing in dispersions e.g. of pigments, catalysts or device structures, influence disease through the attraction of viruses to cells and also cause potential toxic effects through nanoparticle interference with biomolecules and organs. The problem is to understand these small forces which pull nanoparticles into intimate contact; forces which are comparable with 3kT/2z the thermal impact force experienced by an average Brownian particle hitting a linear repulsive potential of range z. Here we describe a new method for measuring the atomic attractions of nanoparticles based on the observation of aggregates produced by these small forces. The method is based on the tracking of individual monosize nanoparticles whose diameter can be calculated from the Stokes-Einstein analysis of the tracks in aqueous suspensions. Then the doublet aggregates are distinguished because they move slower and are also very much brighter than the dispersed nanoparticles. By finding the ratio of doublets to singlets, the adhesive energy between the particles can be calculated from known statistical thermodynamic theory using assumptions about the shape of the interaction potential. In this way, very small adhesion energies of 2kT have been measured, smaller than those seen previously by atomic force microscopy (AFM) and scanning tunneling microscopy (STM).