What good do colonies do for my domain?

If you establish a 5 province colony in both North and South America and they grow further by themselves you actually have quite a solid investment. In your original question you seem to have overlooked the Trade Power transfer that you get from your colonies.

Just keep in mind that the trade from the West is distributed among the 3 CoT on the West coast of Europe unevenly. If you are playing as Portugal for instance, having a colony in the Northern US is a lot less beneficial to you.

In the end, the additional Trade Value generated by the colonies once they have expanded, transferred to your home Center of Trade in part because of the "free" trade power you get from your colonies, should give you a pretty nice return on the investment you provided.

If you do need to have a faster return of investment you can always raise the tariff levels, although this does mean a higher Liberty Desire.

I believe all of which you describe is intentional, by design, to prevent colonization from becoming too powerful. Certain countries would have a too easy time (e.g. Portugal).

Note that (without mods), colonies only are created in the Americas, not in Africa or Southwest-Asia. This correlates with the difficulty of creating a colony - the Americas are vastly easier to colonize since they got far fewer negative factors (tropical etc.). Until a recent patch, you'd even only get a 1% settler increase in most of Africa, whereas the Americas regularly had 20% or more - that is a difference of several years of time taken to colonize.

You will notice another negative aspect soon: You colonies tend to drag you into war with the other col powers (mainly England, France, Spain, Portugal, or more precisely, their respective colonies). This can be annoying, but I like to think it makes the games more interesting and adds a certain balancing element to the European theater.

Update: Note that colonies do not add to overextension.

To extend on what @Richard-ten-brink said, yes, colonies give you 50% of their trade power to you in all nodes where they have power. This is fantastic and as time progresses and they cover more of their colonial regions you'll find the wealth they bring to your home node (provided the colonies align with your trade flow) will grow to ridiculous proportions.

If you want even more money aside from trade wealth (which ends up being the highest at the end of the game usually), then you can up the tariffs, which makes them more likely to seek independence. You can also increase your tariff efficiency with idea groups and policies http://www.eu4wiki.com/Policies See here for tariff information. http://www.eu4wiki.com/index.php?title=Colonial_nation&redirect=no#Tariffs

I more recent patches colonial nations have been more likely to actively join in your wars, even in Europe. I've had instances where my Mexican and Caribbean nations have sent fleets with armies into the Mediterranean and laid siege to Italian and Croatian provinces.

As for the cost vs benefit for growing colonies, I advise you start small and don't have more colonies than you have colonist unless you're swimming in cash (Portugal can do this with relative ease).

Most Colonies are more for their value of trade then anything else (they also give you a large boost to your naval force limit).

The tariffs you get from them are...ok...but once they get high enough (discounting bonuses from ideas and policies which don't increase liberty desire) it starts making them rebellious.

Now...if you have colonial mexico on the other hand and took everything in Central Amercia where the Aztecs were...that is a cash cow because it has so many gold mines which fill up and deposit rather large lump sums of cash periodically as gold-shipments something around 100-200 gold per year or so.

I typically expand a colony in each region till it hits 10 cities for the +1 merchant, and then ignore it while i focus my efforts towards Africa and Asia with trade-companies, while working to get a monopoly on all of the end-node trade regions in Europe.

And so many colonies gives you a large amount of trade power to help steer trade to where you can most benefit from it.

due to the distant overseas penalty there is very little point to hold that territory directly since even the trade value is decreased, but putting under the control of a colony/vassal/trade company/protectorate, you can get SO much more money from the trade value then holding it normally.