Stief, I might have fixed the problem. On the LW support page I read
Apple acknowledges Mac OS X 10.3.9 Java issues., leading to some articles on how to fix this.
Typing some strings of text into terminal everything seems to be cool now. My memory doesn't get used up as before. Still there is a percentage labelled "inactive", which I don't understand why (after all I've got the RAM in there to BE actice) but the free RAM doesn't get used up anymore. Let's hope it stays like this.
Greez,
Bman