It sounds like a couple of your belt pulleys have come loose giving you a bit of backlash. I would go around the machine and check all of them for tightness as this would cause the double engraving but you wouldn't notice it when cutting as you are only following 1 line.
There is a lot of difference between cutting and engraving if you use bidirectional engraving as the speeds are far greater and more backlash will show up, or even belt stretch, if the belts are small enough.
That's my best bet, a loose pulley on each axis.
Rich.
I am not completely useless.......I can always serve as a BAD example.