a covering (usually of cloth) that serves as a roof to shelter an area from the weather
A canopy can also be the uppermost layer in a forest formed by the crowns of trees, which is what is described in this example sentence. Note that a good portion of the words used in this story deal with plants, flowers, and the growing of vegetation, even if at times they are used figuratively. Compare with sprout, bloom, blossom, and flourish.
Their disappointment at not having found Minli forced them to admit their exhaustion, and they had slept under the canopy of tree branches during the day, leaving their silver goldfish as a guardian.
Like "sprout" the word "bloom" is used figuratively. The two verbs are almost synonymous, but "sprout" refers to the beginning of something growing (whether it's vegetation or gossip), while "bloom" refers to a later stage of development that's often connected to more beauty (which could come in the form of flowers or more details in the stories).
Stories of their happiness spread like seeds in the wind, sprouting and blooming everywhere, until finally even young Magistrate Tiger heard of them.
the condition of being honored (esteemed or respected or well regarded)
Compare with "reverence" in the list for Chapters 1-12. The example sentence describes the esteem as one that "rivals the gods"--which makes it synonymous with "reverence." But "esteem" is usually less powerful than "reverence" since it can describe an attitude of admiration or approval between strangers.
The adults are loving and faithful, the children are gracious and respectful, and all honor the grandfather with an esteem that rivals the gods.