How to calculate the amount of weight my plane can takeoff with? This is how I approached this problem-

My takeoff run is limited. So, depending on my configuration I calculated the maximum possible velocity I can attain in my groundroll. I assumed that at the end of the run my lift should be greater than the weight I want to carry. So I computed the lift I generate at the end of the groundroll. I got the CL value from xfoil for my angle of incidence. Would this method give me a rough estimate of the total weight my plane can carry?
Yes, you can do your equations at OEM (Operating Empty Mass) and get your ground distance. Then you can calculate the same for different mass values (your OEM+your payload), and generate a distance vs mass. Since you know how much distance you have (including any safety factors), you can see what mass you can take off with. Or work backwards from the same equation, set the maximum distance you allow, and work back to your mass value.

Keep in mind this will not tell you whether the airplane is structurally strong enough to carry that weight, only if it can take-off with it. Structural calculations are a bit more complex than this. Also, you might want to do similar calcs for landing distane as well!