Is there any way to increase the size of the log window (the one which shows the die rolls etc.) at the bottom left of the screen? I find myself scrolling up all too often, and at 1920x1080 I do have a bit of screen real estate to work with...

Grab the bar at the top of that window (there's a small up-facing arrow), and move your mouse upwards. You can even make it as tall as whole screen.

Guess I played too much Baldur's Gate, where clicking the arrow at the top cycled between sizes.

Annoyingly, it seems to reset to the default size every time I load a game. Is there any way to change the default?

Not that I'm aware. NWN has a lot of features that are great, but there are some that they just didn't think of at the time they made the game. Another that I find annoying is the fact you can't drag the open inventory/map/spell windows wherever you want them. Still, the HUD isn't all that bad considering the age of the game.