Answer:
The beam waist mostly depends on the wavelength of the laser, because the beam waist cannot be larger than the diameter of the wavelength.
The following equation shows that the wavelength and the beam waist are directly proportional.
where ω is the beam waist, λ is wavelength, n is the index of refraction, and z_R is Rayleigh range.
Considering the electromagnetic spectrum, blue light has a smaller wavelength than infrared light, hence the light from blue laser forms a narrower beam waist than that of infrared.