This is as much a mechanical project as an electronic one. An LVDT is a great sensor, but you will need a spring to weigh against, to create a deflection for the LVDT to sense, and some means of mounting it with very little hysteresis. The ideal spring material is NiSpan C, since its spring rate doesn't change with temperature and it has the lowest mechanical hysteresis of any metal. An alternative method is the singing wire, where a wire (of NiSpan C preferably) is made to resonate in a magnetic field by a current sustained in a feedback loop. The frequency of oscillation is proportional to the square root of the tension in the wire. It is a very wide dynamic range technique.

Steve