Will Thrust on Rotor (Main) increase with altitude?
I presume that OP means torque on the rotor, since thrust must always compensate weight to maintain altitude. Thrust T, torque Q and power P equations for momentum theory in the hover:

$$T = C_T \cdot \rho A (\Omega R)^2$$

$$Q = C_Q \cdot \rho A (\Omega R)^2  R$$

$$P = C_P \cdot \rho A (\Omega R)^3$$

with $C_Q$ being identical to $C_P$.

At any altitude, thrust must equal weight. Air density $\rho$ decreases with increasing altitude, so $C_T$ must increase with increasing altitude which it does linearly.



Above graph from Leishman shows the relationship between $C_P$ and $C_T$, which can be approximated as:

$$C_P = \frac{\kappa \cdot {C_T}^{3/2}}{\sqrt{2}} + \frac{\sigma \cdot {C_D}_0}{8}$$

with $\kappa$ = loss factor and $\sigma$ = blade solidity.

So power required increases with $T^{3/2}$, and therefore increases with increasing altitude. Since $C_P$ = $C_Q$, torque does as well. Note that the weight at altitude has decreased due to the fuel burn required to reach higher altitude, which will compensate some of the additional torque required.