Why is equilibrium achieved at different stages of a reaction?

In other words, I want to know why some reactions attain equilibrium early in the reaction while some reactions obtain equilibrium at the end of the reaction.

Why is this the case?

The rate constant, which is approximated by the Arrhenius equation, is dependent on the Activation energy, Ea, and temperature, T. Activation energy can be lowered by using a catalyst (if any). $$k = A e^{-E_a/(R T)}$$