If friction is caused by the reaction of molecules between the two surfaces, why doesn't a force act when you lift the object?

It does!

In most cases the force is too small to be noticable however it is there. I spent a happy few months measuring the friction between carbon whiskers, and the adhesion force between the whiskers was large enough to cause a noticable deformation of the whiskers when I separated them. In fact you had to add the adhesion force to the applied load to get a correct value for the friction coefficient.

For large objects the force is usually small compared to the weight of the object however in special cases, e.g. very clean surfaces, it is large enough to cause cold welding.