David Drake covers this sometimes in his novels. I want to say it was somewhere in "Hammer's Slammers" where it came up in some detail:
Basically the owning company just needs to control trade.
It's hard to cut off trade on good old planet earth because there are too many parties and travel is relatively easy and hard to control. We rebel against England, and France happily buys our stuff. Or the rebels buy and sell on a black market. It's also hard to cut off low tech trade because you can probably make most things yourself, locally, anyway. I think "trade" is one of those things that's easy to underestimate, though, especially as tech levels go up. A colony with no trade may be self-sufficient in the sense that they aren't going to immediately die but it's a very vulnerable (and dull) state to be in.
No trade means no help in a disaster. One bad year of crops and everyone dies. It means anything you can't produce locally just can't be had for love of money -- this could be high tech gear (you need computer chips but a "computer chip factory" is not something you can just locally produce with blacksmiths) or it could be things that simply are not available locally (e.g., maybe the colony has tons of iron but no form of coal and it's hard to grow enough trees to act as carbon/fuel).
So, at least in Drake novels, the way colonies are kept subservient is by simply not supplying them with the things they need to "tech up" or expand their product lines. Let them produce all the raw materials they want but never sell them or help them build the things they need to turn those raw materials into a finished product.
Keep control of the spaceport and ideally just don't allow anyone else to trade with the colony that doesn't go through your company. e.g., Amazon decides to make a Mars colony but Amazon controls the space port therefore nothing goes in or out without them knowing about it. If they don't want the colony to make computer chips (or laser drills or insert-high-tech-gizmo-here) then they're not going to be able to because they will never have the technology or parts for it.
There's also something of a sense of cooperation between the major companies that can afford colonies: we don't help your rebels if you don't help our rebels. So the rebels rise up and take the space port but they can't actually get anyone to trade with them. Small timers don't have space ships and the few organizations big enough to have space ships have shaken hands with each other. Eventually the rebels back down and let the owners back in because they liked it better when there was trade.
So, in summary, control trade and you control the colony. (At least in "near future tech" terms. If you reach a level of tech where people are flying around in personal star ships, ala Firefly/Star Wars, then it's more like "old earth" where travel is too easy, smuggling is rampant and it would be very hard to control a colony without direct military threats.)