If I read this correctly, you are going to need a first order linear differential equation to model weight as a function of time. We may express this as the initial value problem:
is weight as a function of time .
is daily caloric intake (assumed constant).
is the caloric expenditure as a function of weight (for simplicity, height and age are held constant).
where the constants are:
Multiplying through by we have:
Using the initial conditions, we find: