What does you gcode look like?
Is it a load of linear moves (G01)
Or is it a mixture of linear and arc motion G01 + G02/G03
Constant velocity tries to attempt to maintain a constant velocity but there are limitations as to how constant velocity can actually be maintained..... Think of it this way...
You're running down a road flat out. Can you change direction 90 degrees still running flat out..... Exactly 90 degrees! If your flat out is walking probably, if your flat out is Usain Bolt probably not.
Ok option a..... Move slower so you can turn 90 degrees exactly..... Option b slow down so you can turn exactly 90 degrees.
Mach3 is not very good at defining what Constant Velocity actually is ..... what is the relationship of how slow is slow enough? How much in advance of the junction or corner does it slow down? Is it different for G01>>G01 or G01>G02/3 or G02/3 >> G02/3 or G02/3 >>G03/2 or G02/3 >> G01 motion?
Try to use the motion planner effectively by using linear motion where the move is linear and arc motion where the motion is an arc. Use roughing cuts and finishing cuts. Consider using exact stop with finishing cuts if precision is required. That way the unknowns / undefined elements of the motion planner and constant velocity are removed or minimised.
Jerk or jolt is something slightly different and is to do with trapezoidal acceleration which all lower cost motion planners (mach3/mach4 etc) seem to do and is related to your machine setup of drive mechanism, microsteps etc.