Hi,

This is a good question.

The debugger does not store the large "when hit" message strings on the arduino, instead if keeps them on the pc and shows the correct text for the breakpoint numbered 0-infinity. Breakpoint 1, 2 3 etc.

However, the debugger does carry a memory overhead which can increase depending on what your code uses. For example if your code already uses the serial port then the additional overhead of the debugger using the serial is zero otherwise it is the serial buffer + some other arduino stuff.

Each breakpoint will cause a small memory increase depending on the specified break condition and number of {expressions} being watched. It also uses small 4 byte strings as packet terminators so could be more efficient in this area.

Generally speaking if you have your own hardcoded serial.print() commands commenting them and replacing with a breakpoint when hit can save a huge amount of arduino memory. This tends to benefit newer uses or project where code is often full of diagnostics/pint messages. 

From what you have said, I suspect your memory usage is very highly tuned and in that case the debugger might not be a viable solution.