How heavy are antique firebacks?

They take considerable effort to move. Most require two strong adults to lift safely. Moving them across a tiled hearth requires care. Never slide them directly on the stone.

I have a wide fireplace with a shallow grate, and I was wondering if I can put any fireback behind it or if the dimensions need to match exactly?

The plate needs to sit comfortably within the brickwork. You want a gap around the edges. Expanding metal can push against the masonry when hot if it fits too tightly. Width matters more than height. Ensure the backplate covers the area directly behind the main heat source.

Can a cracked fireback be repaired?

Cast iron is notoriously difficult to weld. Some specialists can stitch or braze a crack, but results vary. Many cracked plates are simply propped firmly against the back wall. As long as the pieces hold together, they still protect the brickwork.

My builder told me to paint the old fireback we found in the chimney breast but I don't want it to smell when the fire is lit.

Standard paint will blister and give off fumes. People historically used black lead, though modern grate polishes work similarly without the hazards. Polish is applied cold with a brush and buffed. It restores a uniform dark grey finish and stops rust forming during damp summer months.