Firstly, a plane can be less heavy, not less heavier. BUt I digress...
As we all (I hope) know, we can get more lift from an aerofoil by increasing its angle of attack (AOA). This works up till a point, beyond which the airflow can no longer stick to the upper surface of the aerofoil, so it will become turbulent, and the aerofoil will stall.
To keep an aircraft flying level, lift must exactly oppose weight. Therefore, a [more] heavier aircraft will need more lift to prevent it from descending.
Weight = lift
Lift = Coefficient of lift x 1/2 x Area of wing x Air density x Velocity squared
For an increased weight, we need to increase lift. To increase lift, we can increase any of the values on the other side of the equation. 1/2 is a constant and air density is usually constant. We can change the area of the wing (can anyone say 'flaps'?) or the velocity. However, as we are discussing stall speeds here, we wouldnt be increasing velocity, and we would want to leave the plane in one certain configuration, therefore we would concentrate on the Coefficient of lift.
To be honest, I dont know how this is calculated. All I do know is that it takes AOA into account. Cl is higher as AOA increases, up to a point (the stall). To maintain a certain value of lift, we can decrease velocity as long as we increase another value. For this, we will keep 1/2 x air density (rho) and the area of the wing the same, only changing Cl.
I now refer you to this basic graph: http://www.aviation-history.com/theory/lift_files/fig9.jpg
As you can see, the Coefficient has a maximum value that it can take. To keep the lift generated constant, we can decrease the velocity, but would have to increase the Cl. This works fine, up until this peak. When the critical AOA is met, the aerofoil will stall, and the Cl will decrease (this is where the graph peaks). Now, both the velocity and Cl are low, meaning that lift generated is low. This means the plane descends (stalls).
A heavier aircraft needs more lift. Therefore, for any value of Cl (which doesnt change depending on the aircraft weight.... only the shape/AOA of the aerofoil) the velocity must be higher. Therefore, you can reduce the velocity to a point where Cl must take its maximum value in order to balance out weight. This is the stall speed. A lighter aircraftt, however, doesnt need as much lift to remain aloft, therefore the velocity/Cl (AOA) can be reduced further. The velocity at which Cl must take its maximum value is therefore lower.
Stall speeds are determined by the speed at whic the aircraft stalls when maintaining level flight. A heavier aircraft will need to be travelling faster than a lighter one at a certain AOA in order to stay aloft (or have a higher AOA for a certain speed).
Stall speed is also related to wing loading. An aircraft in a certain configuration has a fixed wing size. If you increase the aircrafts weight, the wing loading (amount of weight each area of wing has to support) increases, increasing stall speed. This is also what happens in a turn (a 60 degree bank at a level altitude will generate 2Gs, therefore each unit area of wing will be supporting twice what it normally does. This increases stall speed, and is why you have to be particularly cautious with your airspeed in a steep turn).
Anyway, I hope this answers your question (moreover, I hope what I just wrote is correct!) though if Im honest, it wasnt really clear what you were asking.