Do they naturally grow slowly? Are they affected by influence or other parameters?
As far I can determine border grow depends on population number on a planet.
IE If there is a 10 size planet then it will have border range corresponding to 10 population. Mind you that is just baseline border growth. 25 size is the highest you can go so you will get most influence from those.
I notice that border grow correspond with how many population you have on planets.
There are technologies that will boost how much range your border grow.
You can also build frontier outpost to expand in a certain direction but it has a draw back. Very tiny border grow and upkeep of one influence point a month.