Working out 6 weeks without rest days ??
Its would be unhealthy and bad if you don't listen to your body if you continue to exercise when you are fatigued or sore. Sometimes it might be better to just do a low impact workout and low intense stretches if you feel the need to exercise.
Your muscles wont have time to rest, repair, rebuild and burn the fat...u should rest atleast 1 day a week...maybe 2