Well pump with 15A fuses on a 20A circuit?
Fuses and breakers may have different trip/blow curves. 

Disconnect switches are for reasons other than merely fusing. Among other things so the person servicing a machine has line-of-sight to the person about to throw the switch on. 

You can change the breaker if you like, but there is actually an exception in code for certain motor loads, to allow overbreakering of the motor to avoid false trips on startup. So I wouldn't be surprised if the 15A breaker had nuisance trips. This exception activates if certain mathematical formulas are satisfied; it is not carte-blanche to up-breakering any motor that trips. 

Given that both are fused this may be a 240V motor. The white wire is the other hot.  Under contemporary Code it is supposed to be marked with tape, but traditionally this was optional if the usage was obvious.  The fact that it is not obvious to you is precisely why they changed the Code.