Can mass be measured without involving weight

Does the determination of mass always have to go through weight?

Yes, there are three main properties of mass:

1) Affect by and on gravity
2) Inertia
3) Equivalence in energy

When you measure the weight, you are using (1). You could reasonable use (2), for example by colliding an object of known mass with one of unknown mass. Using their measured initial and final velocities, you could calculate the unknown mass by conservation of momentum.

It would be rather difficult to measure mass by using (3). You'd have to annihilate all the mass you were measuring. But particle physicists do it that way on tiny particles.

Weight is just easy because F=ma is a simple equation. We know the acceleration due to gravity from Earth and we measure the weight (or Force) and then solve for mass. There isn't much of a reason to find mass by any other method. But you could find the objects density by seeing what percentage of the object is above or below a liquid of known density and then calculate its volume by using liquid displacement.

Yes. Density = Mass / Volume.

You can calculate volume and then use the force of buoyancy to calculate density of an object. Once you have those two you can calculate the mass of the object.

Another thing to consider is that Mass and Weight are one and the same thing on earth. Weight = Mass * Gravitational pull.

So it'll be very difficult for you to calculate weight without mass.

Not neccessarily,you could totally find the mass of an object with out its weight. It also depends on the question,
Sorry but do you have a legit example?

yes beacause the force of gavity acting on the mass would give it weight