What Causes Left Hand And Leg Weakness?

hi. i am 40. since few years i have been felling that my left hand and left leg are weaker than my right hand and leg. i am not getting same strength in my left hand and leg which i am getting from my right hand and leg. is it a syndrome any of serious disease?. my weight is 68 kg. i have been suffering from hypothyroidism since over 11 years. doctors have prescribed me to take 3 thyroxine tablets in a day.