In IR spec, it kinda makes sense that single bonds (e.g. C-C) would require less energy to move to a higher molecular energy level, than double/triple bonds (C=C) etc. But what I don't get is how come a higher molecular mass molecule doesn't need as much IR energy to 'stretch' than lower mass molecules? Wouldn't lower mass molecules be able to 'stretch' with less energy because there is less mass that needs to be excited?
In quantum mechanics, we model chemical bonds as springs. Then the restoring force is -kx and the potential energy is 1/2 kx^2, where x is the extension of the spring and k is the spring constant (just a constant). Classically, these springs vibrate at a particular frequency given by 1/2pi * sqrt(k/m) (I'm not going to prove that completely, but if you want to try, use F = -kx = ma, rearrange to get a = -kx/m, use a = d^2 x/dt^2 = v dv/dx to show that x is a sinusoidal function of t, notably x = A cos(sqrt(k/m)+constant))
The keen pedant will notice I used m instead of the reduced mass, which is actually what you should have in the above formula.
Using principles of quantum mechanics, it can be shown that quantum mechanical springs can only absorb light at the above frequency. So there are two factors at play here: the (reduced) mass of the system and the strength of the chemical bond (k is a measure of the strength of the spring). For heavier molecules, the mass increases and the frequency of oscillation (and hence of light absorbed) drops. This makes sense because for a given spring, heavier masses will accelerate slower.
For lower mass molecules, they now oscillate faster because of their lower mass.
You've misunderstood how IR works. It works not because of the energy required to stretch the bond; rather, it works because the frequency of light that can be absorbed is the same as the frequency of oscillation.