Assuming a windows system, there's a file called "vmparams" in the starsector directory.
Editing that with any text editor (notepad will do but notepad++ will be better, wordpad would probably be fine too) and replacing this: "-Xms512m -Xmx512m" with this: "-Xms1024m -Xmx1024m", then save and use the launcher as usual.
You could go up to -Xms2048m -Xmx2048m if you have the ram, but in my experience this means the launcher won't start properly because Java fails to allocate all that memory. To fix that, you may need to replace the JRE with a 64 bit version. This basically involves downloading a recent 64bit JRE, and copying it over the one in the starsector/jre folder. If that's too complex, try numbers in between 1024 and 2048 until something works for you.
Finally: Loading a save seems to take quite a bit more memory than actually playing the game, presumably because the game doesn't keep -everything- in memory all at the same time, but loading needs to do initial setup on everything at least once.