WAR means "Wrestling And Romance", or alternatively "Wrestle Association R". The J-1 Heavyweight Title was the promotion's only heavyweight championship. It's maybe not too far fetched that J-1 could mean "Number One of Japan" or something like that. As is common practice, the titles were abandoned when the promotion closed in 2000.
"Lying is the most fun a girl can have without taking her clothes off" Patrick Marber, Closer