All 3 Uses of

delicacy
in
Brideshead Revisited

It was characteristic of an old, atavistic callousness that went with her delicacy that, even at this crisis, she did not think it unreasonable to put Sebastian in Rex's charge on the journey to Dr. Borethus, and Rex, having failed her in that matter, went on to Monte Carlo, where he completed her rout.†
p. 217.9

It had been an afternoon of low cloud and summer squalls, so overcast that at times I had stopped work and roused Julia from the light trance in which she sat—she had sat so often; I never tired of painting her, forever finding in her new wealth and delicacy—until at length we had gone early to our baths and, on coming down, dressed for dinner, in the last half-hour of the day, we found the world transformed; the sun had emerged; the wind had fallen to a soft breeze which gently stirred the blossom in the limes and carried its fragrance, fresh from the late rains, to merge with the sweet breath of box and the drying stone.†
p. 317.6

Definitions:

(1) (delicacy as in: eat the delicacy)
something that is rare or expensive -- usually a prized food
(2) (delicacy as in: discuss with delicacy)
care and gentleness -- especially speaking or acting with sensitivity and tact
(3) (delicacy as in: offend her delicacy)
the quality of being easily hurt or damaged

(often referring to the fragility of someone's emotional well being when it is easily distressed by something that is offensive or disturbing)
(4) (delicacy as in: delicacy of the brushwork)
pleasant subtlety or fineness