Motivated by spin glass theory, I will present the study of the overlap between two particles chosen according to Gibbs measures in a branching Brownian motion. In the case of two Gibbs measures at the same temperature, the behavior is the same as in the case of i.i.d. energies. For different temperatures, the mean overlap is strictly smaller for the BBM and one can quantify this difference in some regime. This is based on joint works with Benjamin Bonnefont and Olivier Zindy.