All 4 Uses of

reflect
in
The Witch of Blackbird Pond

"There's a well behind the house," said Hannah. "Draw some water and wash thy face, child."
Kit let the bucket down, leaning over to watch it meet the far-off circle of reflected sky.
p. 93.2 *

reflected = shown back (an image as on a mirror or shiny surface)

Now some men, Kit reflected, could pick up a ball of yarn without looking ridiculous.
p. 120.1

reflected = thought

John is a part of the family already, she reflected. We have all come to love him.
p. 121.5 *

John took off his hat, leaned his elbows on the fencepost and stood gazing reflectively back at the Meadows, the wind stirring his fair hair.
p. 138.5

reflectively = thoughtfully

Definitions:

(1) (reflect as in: reflect in the mirror)
show an image back (on a mirror or other shiny surface)
(2) (reflect as in: reflect American Values)
to show something -- such as to demonstrate, express, or represent
The exact meaning of this sense of reflect depends upon its context. For example:
- "She says the immorality in the movie reflects American values." -- expresses or represents
- "It reflects the selfishness she had seen growing for years." -- demonstrates
- "She did not reflect the panic that surrounded her." -- demonstrate or show indication of
(3) (reflect as in: I want to reflect on it.)
think carefully -- possibly aloud or in writing
(4) (reflect as in: reflect poorly on the school)
influence opinion

This word is often used in a phrase like "reflect poorly on/upon...." Although we define this meaning of reflect as "influence opinion", the use of "upon" or "on" might feel more natural if you think of it as "casting a shade of good or bad upon/on" something.
(5) (reflect as in: reflect the light/heat/sound)
bounce back (rather than absorbing)
(6) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

See a comprehensive dictionary for less common meanings of reflect.