Stewart, it does sound like your springs are likely worn out if they are convex and the body is sitting at different heights side to side.
Front springs arching upward is definitely not the way they should look. I'll see if I can get a picture of mine. They don't have much curve at all. The truck drives and handles just fine so I don't think they're worn out. It spent its working life on a farm but it hasn't been used to pull a trailer or do any seriously heavy work that I can tell.
As you can see, there is only a slight arch in the front springs of my truck. Certainly they have settled in the last 73 years but they're still springy and the truck tracks true so I don't think they're shot.
1950 Chevrolet 3100 (Ol' Roy)
1939 Packard Standard Eight Coupe (The Phantom) | 1956 Cadillac Coupe de Ville (The Bismarck) | 1964 Ford Galaxie 500 coupe |1966 Ford Mustang (Little Red) | 1969 Pontiac GTO (The Dishpit) I 1979 Ford F-100 | 1976 Ford F-150 (Big Red) | 1995 Ford F-150 (Newt)