[throwaway283719]

There's a fun piece of math you can do with this model. Given the relation

  w[t+1] = w[t] + (c[t] - alpha * w[t] - beta * d[t] * w[t]) / 3500

and assuming c, d are both constant (i.e. assume they are your long-run average of calories consumed and exercise done) you can solve to get

  w[t] = c / (alpha + beta * d) + const * (phi ** t)

where phi is a number smaller than 1, and const is some constant that depends on your initial weight. Over time, the phi t term decays away, and you are left with your long-term stable weight,

  w = c / (alpha + beta * d)

Using c = 2000, alpha = 12.5, beta = 0.63 and d = 0 you get a long-run stable weight of

  w = 2000 / 12.5 = 160 lb

On the other hand, if you eat 2500 calories per day but run five miles, you get

  w = 2500 / (12.5 + 0.63 * 5) = 160 lb

so if you want to eat an extra 500 calories per day, you should run 5 miles per day.

It'd be interesting to see how accurate this is.

[koobz]

As you gain weight, you burn more calories passively. I'm 155lbs and could imagine it being difficult walking around with what amounts to nearly a barbell and two 35lb plates should I be in the extremely obese range for a man my size.

Assuming no lifestyle changes - I might be less excited to ride my bike with a 115 lb bag on my back - you should reach some sort of thickquilibrium.