The weak force is the force that induces beta decay via interaction with neutrinos. A star “burns” by a nuclear fusion process. Three of those processes are proton-to proton fusion, helium fusion, and the carbon cycle. Here is an example of proton-to-proton fusion, which is the process our own sun uses: (two protons fuse -> via neutrino interaction one of the protons transmutes to a neutron to form deuterium -> combines with another proton to form a helium nuclei -> two helium nuclei fuse releasing alpha particles and two protons). The weak force is also necessary for the formation of the elements above iron. Due to the curve of binding energy (iron has the most tightly bound nucleus), nuclear forces within a star cannot form any element above iron in the periodic table. So it is believed that all higher elements were formed in the vast energies of supernovae. In this explosion large fluxes of energetic neutrons are produced which produce the heavier elements by nuclei bombardment. This process could not take place without neutrino involvement and the weak force.
Thanks for the detailed explanation of how the sun nuclear process works. As you show, this is a natural function due to the chemical and nuclear constitution of the elements involved. This process has nothing to do with the 'assembly' of anything as claimed by Dr. Stochastic. Thanks for the clarification.