Ha, our posts crossed! That Buddhist statue is a lot larger than I thought.
That is a big sword, and the fuller is obviously intended to help reduce the weight of the blade. I've had other large SE Asian swords that were apparently used by powerful men in the vanguard of an attacking force, basically carving a hole in the enemy lines for other troops to advance. I suspect that this one was used for similar purposes.
I'm going to say Thai or Lao for its origin, probably Thai. The fuller is atypical but clearly serves a purpose given the size of the blade.
That hilt still bothers me from a practical viewpoint.