Just as I attribute being a living organism equally to my heart, lungs, et al., I attribute who I am equally to being short, absent minded, gay, et al..
It's my philosophy that all things contribute, in a way, to each other, culminating the being.
That is to say, I don't see anything "simply as another characteristic," compartmentalizing traits like I used to separate the food on my plate, not wanting the items to touch, when I was younger.
Relating such to happiness, I believe segregating one's traits creates a situation similar to what is said in Matthew 6:24, "No man can serve two masters: for either he will hate the one, and love the other; or else he will hold to the one, and despise the other. Ye cannot serve God and mammon."
Happiness comes in accepting everything of oneself as oneself, no trait greater than or really separate from another; otherwise, one will tend to love one trait and despise another.
This includes our weaknesses.
Like I tell my students, one needs to accept and be happy with where one is. Such does not mean one should never expect to improve, but understanding where one can be, what one can become, must neither negate nor degrade where and who one is.
Otherwise, one's progress and happiness are impeded.
*yes, I add an apostrophe-s to singular nouns that end in s.