So, to provide some detailed information,
(1) FAA when doing an investigation can see the diagnosis codes used by your doc to bill the insurance company. Omission is not an option. If you do and an investigation occurs, you lose your PILOT certificate. Also remember what they did to Martha Stewart. Google her if the name rings no bell.
(2) Is there a psychiatrist on your healthcare team? It becomes important, depending on the "resolution" of the anxiety diagnosis. FAA is looking hard for alcohol hiding behind anxiety or behind depression.
(3) Depending on the duration of use of weed, the agency may demand provable evidence of abstinence in the form of urines over a period of time. But maybe not, depending on what a qualified external psychiatry expert has to say. Usually to save $$s, I consider starting a proven sobriety program PRIOR to seeing the external psychiatrist.
(4) Depending on what your medical records look like, an "in healthcare system" psychiatrist might do the job. But at the other end of the spectrum is the HIMS investigational psychiatrist, about $3,000. They are the ultimately "credible" external experts: but for that, to keep your powder dry, I would DEFINITELY spend the time cents to probe sobriety over a substantial period of time. See 67.307 for the definition of "abuse" and the two year prohibition.
Bruce