If you are laying mesh, the key thing is to get the mesh in contact with the ground underneath, so if you are laying it over grass then you may need to cut the grass short first. This way the part of the foot the lands between the mesh, rests on the ground, so the weight is evenly spread. The problem comes when mesh is 'floating' so the only part of the foot in contact with anything is the bit touching the mesh - this means a very small surface area takes all the weight.
If it's to stop digging then you can use wider spaced mesh eg 1-2" which gives you bigger holes for the grass to grow through.