I may be misinterpreting, but they way it's worded several times makes it seem like an INCREASE of 4.00 rather than a raise TO $4.00.
It's probably not a raise of $4/hr as that would have been a very large amount, as you point out. Given that the minimum wage in 1977 was about $92 per week I think it's much more likely that the context is an amount per weekly paycheck. A $4 raise on a near-minimum wage paycheck would be about a 4% increase, which is reasonable in the context of Tony's low paying job.