With respect, tim00, the OP first considered stengthening his existing 4x joists. Glueing and firmly screwing additional 2" pieces along the top will contribute to strength and stiffness regardless of the marginal increase in weight. Each joist will have considerably increased I and Z values which will reduce bending stress and deflection. When allowing for the countersinking, it wouldn't be the equivalent of 6x, but it wouldn't be far off.
Yes, in an ideal world, he would put new joists above the existing, but he might have headroom problems. If he is using it as a bedroom already, it will almost certainly not have a certificate, and the OP probably doesn't want to go down that route. All he wants to do is improve the situation structurally, and 2x2 fixed as suggested would do that at minimal cost.
He has no obligation, legal or moral, to any future occupier of the property.
Any new occupier would take it as it is and if in doubt, should get a survey done.