The design is too heavy for the fabric.
When I first started I thought if I only stabilized enough then all would be well. Later, I went to a great seminar by Dini of "Momo-Dini" and she showed how she embroiders on nearly anything, but she makes sure the design is right for the fabric, not the other way around.
I would decrease the density and use a light weight cutaway.
Also be careful not to stretch the fabric when you hoop it.