The phrase "to wean off" means to gradually reduce or eliminate a dependency on something, such as a drug, alcohol, food, or other addictive behavior. Full definition
Slowly wean off of caffeine over three days, and notice how your sleep and stress levels improve! (saragottfriedmd.com)
With peak oil looking increasingly imminent, we need to start the process of weaning ourselves off fossil fuels, and we need to do so urgently. (treehugger.com)
And then very slowly wean yourself off of the meat over time / months. (nutritionfacts.org)