If the elementary particles are cooled, they lose a weight?
Your question is basically in the comments whether BEC changes weight relative to before cooling.
A BEC is formed by cooling a gas of extremely low density to ultra low temperatures.
AS the gas cooles (by laser), the energies of the molecules change via rotational and vibrational transitions.
The answer is yes, because during the cooling, particles, molecules constantly lose rotational and vibrational energies (due to the laser cooling), and thus because of the energy mass equivalence, the gas will lose mass.
When the gas forms a BEC, it will still have mass, and stress-energy thus it will still interact gravitationally.