Zeus was king of the gods, and his lightening bolt was something of a supreme weapon in the clash with the titans.
And yet, Zeus is often depicted as a hen-pecked husband, fearful of his wife.
What power does Hera have over Zeus?
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She's a daughter of Zeus in her own right, and so has some power on his footing. However, I wouldn't say Zeus is a hen-pecked husband. In the Iliad (560-569), Zeus states unequivocally that he is the supreme being of the universe:
Zeus, the cloud gatherer, spoke out in response:
“My dear lady, you’re always fancying things.
Your attention picks up every detail.
But you can’t do anything about it,
except push yourself still further from my heart,
making matters so much worse for you.
If things are as they are, then that’s the way
I want them. So sit down quietly.
Do as I say. If not, then all the gods
here on Olympus won’t be any help,
when I reach out to set my hands on you,
for they’re invincible.”
Zeus finished speaking.
Ox-eyed queen Hera was afraid—so she sat down,
silently suppressing what her heart desired.
That said, Hera is his wife, so why deliberately incur her wrath? That's the real reason to hide affairs, human or divine.
I have researched a lot of things in ancient mythology, but I can not pinpoint you on specific texts. I can only give you my opinion.
To understand gods, you have to understand human. Follow the nature of that relationship. A human man has a wife. The wife is weaker than the man. Man has physical strength and if woman sees an enraged man, she will fear him and suppress her feelings and her speech. On the other hand, if a woman realize that her man was cheating her with another woman, she will envy and fill her heart with so much rage that even men would fear her. If a woman would have to fight for her child, and the feeling is not flight but fight, we all know that we should not underestimate women. They might lose, but the battle would hurt a lot.
We have also seen women commit crimes for their lovers. Either murder their husband, or their lover, or both, either pull the strings to destroy their lover, or their man, or both.
Let's go back to Zeus and Hera, the perfect couple. Perfect through the representation of the whole imperfection of that relationship. Whoever would question the perfection of that marriage would be doomed to Hera's wrath. Note that down, Hera's wrath.
Zeus having sex with mortals. That made Hera furious too. So what does Zeus prefer? A silent or a furious Hera? Neither of them, but surely he would prefer the furious one. Because Hera in silence is unpredictable. She sent snakes to kill Herakles.
Herakles, in greek ΗΡΑΚΛΗΣ, means 'Hera's Glory' (from the words ΗΡΑ, ΚΛΕΟΣ) and was given as a name so Hera would not throw all her wrath on him. Of course Hera did not fall for that. She haunted him. And Hera did a lot of smart and malicious things against Zeus lovers.
Was she fair? Was she good? Was she evil? Who cares? She was a woman in envy. And that EXACTLY is the power Hera had and Zeus didn't wanted to play with. Because that is what Ancient Greek myths is all about. Human and his imperfection glorified and justified in a relative way, during those years.
Also Hera is smart. She is Zeus sister. She has not swallowed Metis, as Zeus did, but still, she can bend the very same rules Zeus set, at her own will. Zeus knows that. Also Hera is the model of the perfect woman. Even if Zeus was cheating her, she never did. That is why she is the goddess that defends marriage.
Hera can cause trouble. Zeus has to keep things in balance. You can see the dynamics here.