Nature of the surface:
When we move on any surface, we apply a force to overcome the interlocking and adhesion of the surfaces. Rough surfaces have a larger number of irregularities. So, interlocking will be more and hence the frictional force will also be more.
The friction is caused by interlocking and adhesion. So, when two surfaces are pressed harder, interlocking in irregularities will increase. Also, the surfaces will come closer and bond formation will be more, therefore adhesion will increase. Hence we can say, as the thrust increases the friction also increases. For example we experience it by dragging a mat when nobody is sitting on it and when a person is sitting on it.