Stief might be better to advise here. hmm, I'd have thought intel MacBooks would definitely be 64-bit. If you were able to install Java 1.6 then that suggests it is a 64-bit machine otherwise you would or should have received an installation error saying unable to install or nothing to install, etc. or so I'd have thought.
Try going to your Java preferences & moving Java 6 (1.6) up the hierarchy of priority of use.
Setting up Java for Leopard. Log out & back into your computer after doing this.
Also use Software update & check for any updates. Repair permissions with Disk Utility.
BTW did you previously have LW 4.18 installed on your machine?