Physical weight, without contact. Is it possible?

Thanks for the reply, I ve tested the first, and the results are very unstable(waay choppy than with contact, no suitable for gameplay).

The second option will create a counterforce on the box, and I want to be able to control the counterforce manually.

The third will fit perfectly for static objects, but not for dynamic ones.

The fourth could be a solution, but I find it rather complex. The point is to apply this behaviour on some objects along any obstacle. Not only a specific asset, and I feel that implementation will bring more problems than solutions as the sockets location/s and the constrain properties will be changing per frame.

Again thanks for the answer, I havent found a solution yet, but I believe that should be one.