We recommend that people maintain a “healthy” level of 50ng/ml. For an average weight person of 150lbs it usually takes 5000iu a day to do this. Now your starting level is not extremely low, so you can probably take 4000iu a day to get to the 50ng/ml. The 2000iu a day will most likely not get you to the healthy level. There are many studies that show at levels below 40ng/ml, your chances for cancer and autoimmune disease rises dramatically!
Yes, weight can affect the dosage. So I would stick with the 2000iu the doctor prescribed and then hopefully they will retest you in two months. We usually recommend 1000iu’s for every 25lbs of body weight.
You can always come back and let me know what your level is in two months. If it is still low or not near 50ng/ml then maybe add another 1000iu for 3000iu total at that time.