In Hesiod's Theogony, he dedicates a part to talking about Hecate's birth and the powers she possesses:
And she conceived and bare Hecate whom Zeus the son of Cronos honoured above all. He gave her splendid gifts, to have a share of the earth and the unfruitful sea. She received honour also in starry heaven, and is honoured exceedingly by the deathless gods. For to this day, whenever any one of men on earth offers rich sacrifices and prays for favour according to custom, he calls upon Hecate. Great honour comes full easily to him whose prayers the goddess receives favourably, and she bestows wealth upon him; for the power surely is with her. For as many as were born of Earth and Ocean amongst all these she has her due portion. The son of Cronos did her no wrong nor took anything away of all that was her portion among the former Titan gods: but she holds, as the division was at the first from the beginning, privilege both in earth, and in heaven, and in sea. Also, because she is an only child, the goddess receives not less honour, but much more still, for Zeus honours her. Whom she will she greatly aids and advances: she sits by worshipful kings in judgement, and in the assembly whom she will is distinguished among the people. And when men arm themselves for the battle that destroys men, then the goddess is at hand to give victory and grant glory readily to whom she will. Good is she also when men contend at the games, for there too the goddess is with them and profits them: and he who by might and strength gets the victory wins the rich prize easily with joy, and brings glory to his parents. And she is good to stand by horsemen, whom she will: and to those whose business is in the grey discomfortable sea, and who pray to Hecate and the loud-crashing Earth-Shaker, easily the glorious goddess gives great catch, and easily she takes it away as soon as seen, if so she will. She is good in the byre with Hermes to increase the stock. The droves of kine and wide herds of goats and flocks of fleecy sheep, if she will, she increases from a few, or makes many to be less. So, then, albeit her mother's only child, she is honoured amongst all the deathless gods. And the son of Cronos made her a nurse of the young who after that day saw with their eyes the light of all-seeing Dawn. So from the beginning she is a nurse of the young, and these are her honours.
The hymn is interesting because it mentions that Hecate has powers over Heaven, Earth and Sea, the three regions of the world, and that she is the goddess most honored by Zeus.
However what I found curious is the fact that Hesiod twice mentions the fact that Hecate is an only child, and says that she is honored despite that, as if it were a disadvantage.
In fact before he mentions the birth of Hecate, Hesiod listed all the other children of the titans, except the children of Cronus, with Perses and Asteria being the only couple to have only a single children , which seems to make the case of Hecate quite unique among her relatives.
On theoi's page I saw this theory : Van Lennep explains that Hecate, having no brothers to support her claim, might have been slighted.
Do you think it could have been because of that?