Dear god, that isn't how anxiety works.
Anxiety works due to stress. People smoke weed, often times, to just puff the stress away. If said people quit after a while, then stress increases due to the person getting too accustomed to using weed to relax themselves.
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An im telling you from some one who smoked it for 4 years; stopped for 3.5 then smoked on an off for another 3; Thats not how it works with marijuana. (Thats 10 years both long and short term use)