Why is the thrust/drag increase much lower at a lower FL with weight the only variable?
At a lower flight level the air density is higher, so a lower lift coefficient can be trimmed and the induced drag is a smaller fraction of total drag. Hence, the mass increase causes a much lower increase in overall drag.

At higher altitude the friction and pressure drag is lower but the induced drag is higher, so increasing the mass will cause a much higher jump in drag.

Now for the numbers: In FL 290 the indicated speed is 155.362 m/s, so the dynamic pressure $q$ is 14,784 N/m². I use surface area $S$ (124 m²) and aspect ratio $AR$ (b²/S = 10.33) from Wikipedia and guess that the Oswald factor $\epsilon$ is 0.8. Now the lift coefficient $c_L$ at FL 290 and 50 tons mass is
$$c_L = \frac{m\cdot g}{q\cdot S} = 0.2675$$
This allows us to calculate the induced drag:
$$D_i = q\cdot S\cdot\frac{c_L^2}{\pi\cdot AR\cdot\epsilon} = 5052\:\text{N}$$
which is just 1136 pound-force; about a third of what you give for FL370. This fits well with the given thrust increase at FL290 which is about ⅓ of the increase at FL370.