Assuming this is in the US, since color conventions may differ elsewhere:
Occasionally white gets reassigned for other purposes. The convention, as you've seen, is that when this is done the end of the white wire should be colored at both ends -- with marker or with tape, typically -- to indicate what role it is now playing.
Red, in the US, is sometimes used for "alternate hot" -- a switched hot such as a traveller, or the second phase of a 240V circuit. As @crip659 said in the comments, on circuits which are 240V only (and don't need neutral in the middle) recoloring white as red allows using two-conductor (plus ground) non-metallic-conduit cable, rather than three-conductor (which would have a real red wire), saving some money.
As far as the two black wires go, I think we'd need to see the pictures to offer any opinions. However, I should point out that if the breaker has only started blowing recently, and those wires have been there for longer than that, they are probably not the cause of the problem. There is either an overload somewhere in the house which needs to be fixed, or the breaker itself is going bad. The former is more dangerous, and more likely.
Unplug and turn off everything on this breaker, and see if you can reset it then. If you can't, the breaker may be bad and replacing it would be the next diagnostic step. If a new breaker immediately blows, the next step might be disconnecting branches of that circuit to try to isolate the problem.
If the new breaker does not immediately blow, turn on things one at a time, maybe one per day, until you find the one, or combination, which causes the breaker to blow. Then fix the bad device, or move the excess load to a different circuit where there's space for it.
In one apartment I lived in, there was a circuit that was apparently heavily loaded; it worked fine under most circumstances, but if I plugged in and turned on the vacuum cleaner without first turning off the stereo system it had about 50% chance of blowing the breaker. Simplest solution was to find an outlet on a different circuit to plug the vacuum into.