I had a save taken immediately after the colonization, so I've replayed it a couple of different ways just to see if I could find some rhyme or reason to freighter behavior. I can't, but here are the results for the record. Again, this is all in the context of a single new colony with no other colonies besides the homeworld, about 3 years into the game. It is difficult for me to imagine how this could be construed as "overexpanding". The new colony was about 1.5 sectors from the homeworld, because that was the *only* continental/marshy planet nearby. There were no independents any closer either.
1) Not immediately building a space port at the new colony is helpful in some ways. A new colony not attempting to build anything appears to generate orders for 300 each of the key strategic resources (steel, caslon, silicon, etc.). However, it's difficult to make any sense of how the freighters source the materials. About half of the orders were shipped directly from the homeworld stocks. But, for example, the freighters ignored the ~40k unreserved steel (price 0.8) at the homeworld and instead decided to fly off to another empire to fill that order, a roughly 3 sector trip including the leg back to the colony. And only the most basic strat resources are ordered this way, so you'll still have to get less common resources (argon, etc.) when you eventually decide to build a space port.
2) Size of the homeworld space port does not appear to matter. I tested by retrofitting my homeworld's MSP into an identical model with the role changed to an SSP. This had no effect on the reluctance of freighters to use the homeworld's stocks.
3) Once a build order is placed, freighters will attempt to find exactly the amount needed to make that build and not attempt to deliver anything more. If a space port build requires 14 silicon, then 14 silicon will be delivered and no more, even it takes 100 fuel to do it.
I have a difficult time understanding how this behavior is a remotely plausible model of private shipping decisions. The more closely I look at it, the more it ruins the whole game for me. The state/private relationship regarding resources is the heart of the game's economic model and much of what makes it interesting for me. Unfortunately it just seems like a really poor model.