So I think Swift owes me thousands of dollars over the past 3 years.

It's best to put your concern in writing to a upper level executive and request a written response.
It might make for a good court/arbitration case if they did not specify that you couldn't get both night and weekend pay.
Did you save the notice of the pay raise way back when? If you're like me, probably not.

When I had my union job I got paid both night and weekend differential so it's not unusual.

You should be getting the extra pay, but be prepared for them to say that you haven't said anything for three years so that meant you were OK with it. The fact that you worked all this time without bringing up the pay discrepancy let's the company know that other drivers will do the same so why should they change?

Don't be surprised if they brought in other drivers to the account and are paying them both night/weekend pay and give you the excuse that they were hired under a new pay package. Schneider is infamous for this.

 

Do you have a specific gate time? Maybe night time pay starts at 16:00 but since your gate is 15:00 you don't get it.