It will in general depend on the shape of the object. If it has a large concentration of mass at the edge you are lifting then the force will be close to its weight; if its mass is concentrated near the other edge then it will be very small.
The general case is solved using the law of levers:
If $d$ is the distance from the fulcrum to the centre of mass and $L$ is the distance to the edge you're lifting, then the force $F$ that you apply is related through the weight $W$ of the object through
at equilibrium. For most symmetric objects, like tyres, the centre of mass will be at the geometric centre of the object, and therefore you will need to apply half the object's weight to hold it, and slightly more than that to lift it.