quantity of heat Q is equal to mass m[g] times specific heat c[J/g/K] times temperature difference Δt[K].

Q = mcΔt [J]

letting cΔt be constant, then 

Q ∝ m.

heat capacity C is equal to mass m[g] times specific heat c[J/g/K].

C = mc [J/K]

c is constant. then 

C ∝ m.

the amount of rainfall precipitation R is equal to mass m[kg] over an area S[m^2] and duration t[hour].

R = m/(St) [kg/m^2/hour]

letting St be constant, then we get

R ∝ m.

, although C and R are intensive variables.