Why did no one suspect Jim?

I really liked this film, but I couldn't work out why no one - Kath included - seemed to suspect Jim. After all, he was going to be married to Kath's sister, they had a child together; and he worked at the docks near to where she disappeared. Yet there seemed to be no suggestion that he was - or ever had been - suspected of any foul play.

"That, - Captain Bligh, - that is the thing; - I am in hell, sir - I am in hell."