In this study, we present a unified motion planner with low-level controller for continuous control of a differential drive mobile robot under variable payload values. Our deep reinforcement agent takes 11 dimensional state vector as input and calculates each wheel's torque value as a 2 dimensional output vector. These torque values are fed into the dynamic model of the robot, and lastly steering commands are gathered. In previous studies, intersection navigation solutions that uses deep-RL methods, have not been considered with variable payloads. Our study is focused specifically on service robotic applications where payload is subject to change. To the best of our knowledge, this is the first study in the literature that investigates intersection-navigation problem under variable payloads using deep-RL. In this paper, deep-RL based motion planning is performed by considering both kinematic and dynamic constraints. According to the simulations in a dynamic environment, the agent succesfully navigates to target with 98.2% success rate in test time with unseen payload masses during training. Another agent is also trained without payload randomization for comparison. Results show that our agent outperforms the other agent, that is not aware of its own payload, with more than 40% gap.