1 Trade Port = $
2 Trade Ports = $$
3 Trade Ports = $$$
This is true, each trade port you build will increase your trade income linearly. However...
Does the number of planets with trade ports make a difference in the amount of $ you make from trade? Does the length of the longest "route" (that white line I'm guessing) have a bearing on trade $$ made?
As you guessed, exactly how many credits that $ stands for can vary based on several things. Research, abilities, planet bonuses, but most importantly the length of your longest trade chain (yes the white line).
For each planet in your chain, every trade port in your empire (even those not on the chain) get a 7.5% trade income bonus, which is basically a free trade research. However, exactly how its calculated is trick. Your trade chain is the "longest shortest" trade route in your Empire. In other words, your trade route will not ignore planets with trade ports to make your chain longer, you cannot let there be shorter paths connecting parts of your chain. Planets that just branch off but don't go anywhere else on the chain are fine, but anything that might be a shortcut you'll have to avoid putting trade ports there.
As complicated as it sounds, its actually pretty intuitive after you pay attention to that white line for a bit.