For simnplicity, assume the aircraft to be at 0 deg AoA when at Vref, for both the light and heavy cases. That allows us to have the thrust aligned with the direction of travel, which simplifies things a little bit.
Consider the forces acting both along and normal to the flight path.
Normal: We have the aircraft lift, plus a component of the weight (cos 3 degs * the weight, in fact)
Along: We have the drag, the thrust, and a component of gravity (sin 3 degs * the weight)
If we assume equilibrium, then:
Lift = W*cos3
Drag=T + W*sin3
In order to see the relationship between T and W for this case, we need to eliminate Lift and Drag. If we assume they are a fixed ratio k for all cases of W (which seems fair for a fixed AoA approach condition), then:
L/D=k
>
L = D * k
>
W*cos3 = ( T + W * sin3) * k
which, after further messing about, gives:
Thrust = Weight * ( (cos3 - ksin3) / k)
Therefore, as long as (cos3-ksin3) is positive, thrust will increase with increasing weight. If it changes sign, then thrust DECREASES with increasing weight.
So, the question is, what is the L/D for the approach case.
If (L/D) sin3 = cos 3 then we have the diciding case
i.e. L/D = 19 (approx) is the dividing case.
So, if your L/D is less than 19 (which seems a reasonable assumption) you should have increasing thrust with increasing weight for a 3 deg glideslope (for the other minor assumptions). But you will need less thrust than in level flight for both cases (of course)
Now, if you assume a rather steeper descent rate the case becomes of more general interest, since the L/D value for the swapover becomes lower (for 10 degrees, it's below 6)