The psychology behind choosing to let one's weird side show?
I think the this question would work as effectively as:
The psychology behind choosing to let one's individuality show?
Human beings are social animals. Social pressures play significant factors in moulding personality.
The term conformity is often used to indicate an agreement to the
majority position, brought about either by a desire to ‘fit in’ or be
liked (normative) or because of a desire to be correct
(informational), or simply to conform to a social role
So assuming "weird" is more likely to be further away from social norms. The more social pressure to be borne. This means a greater courage is needed to be oneself. There are links between self-acceptance, social pressure and depression.
Correlational results indicated that all three trait dimensions of
perfectionism (i.e., self-oriented, other-oriented, and socially
prescribed perfectionism) were associated negatively with
unconditional self-acceptance. Also, as expected, depression was
associated with relatively low unconditional self-acceptance. Finally,
a path analysis revealed that unconditional self-acceptance mediated
the association between socially prescribed perfectionism and
depression, and other-oriented perfectionism was found to affect
depression only indirectly through its association with low levels of
Dimensions of Perfectionism, Unconditional Self-Acceptance, and Depression
Gordon L. Flett, Avi Besser, Richard A. Davis, Paul L. Hewitt
Journal of Rational-Emotive and Cognitive-Behavior Therapy
June 2003, Volume 21, Issue 2, pp 119-138
Gaining self-acceptance, one's individuality or "weirdness" is inversely proportional to the incidence of depression; and also improves the individual's capacity to cope with social pressure to conform. So by accepting one's strengths and weaknesses one is freed from (social and psychological) pressure, improving one's sense of well being.