Building flip up seat - correct hinge
This can be done with a torsion spring, or several other types of spring depending upon your design. Or it can be done with a counter-balance.

The counter balance only requires you to set the pivot point of the hinge forward a bit with a weight on the bottom close to the back of the chair bottom. You can practice with a few designs in cardboard to see how adding a weight to a beam and placing the hinge higher or lower and forward and back until you get a feel for how it will behave.

Drew K