Spherical particles at a liquid interface attract each other and aggregate. The capillary forces at play are well described for a pair of objects, but as soon as many particles interact, no direct calculation is possible and only a statistical approach can account for the global dynamics. Here, we focus on the statistics of clustering of such a system with a long-range interaction which varies during the aggregation process. We measure experimentally and numerically the distribution of sizes as a function of time and exhibit a self-similar clustering mechanism subdivided into two aggregating regimes, with a well-defined transition that we characterize.