I do not understand how a light wave can measure something smaller
than the light's wavelength - although this is apparently done with
some Atomic Force Microscopes and Interferometers such as that to
measure gravitational energy with the LIGO experiment.

(As a secondary question: If it has to do with timing of reflected
wave, I still can't fathom how light could be reflected by something
smaller than it's wavelength)

Appreciate any insights into this.

I. Atomic Force Microscope
The force sensor is commonly made using a cantilever that deflects in
response to the force and is read out by bouncing a laser off the
cantilever. The angle of the light changes with the deflection of the
cantilever. The tip of the cantilever is much smaller than a
wavelength, but the part that reflects the light is much larger than a
wavelength. No mysteries here.

II. LIGO
The light bounces off large mirrors at the ends of the interferometer
arms. These mirrors are huge compared to a wavelength. In its simplest
version, an interferometer gives a response whose amplitude depends
sinusoidally on the difference between the length of the reference arm
and the arm being measured. The period of the sine wave is half a
wavelength. It is easy to measure the position on this sinusoid to a
small fraction of a wavelength. Commercially available laser
interferometers for distance measurement can see motions on the order
of a nanometer. In LIGO, they bounce the beams many times off the
mirrors to decrease the period of the sinusoid, enhancing the
sensitivity, and leading to even more precise distance measurement. No
mysteries here either.

Isn't it the amplitude that is important, rather than the wavelength?

regarding the comment:

Isn't it the amplitude that is important, rather than the wavelength?

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no, the amplitude of light only relates to the number of photons
emitted. the wavelength of the light is what affects the resolving
power of the detector

Let me try to explain.
If you throw a stone in a pond you see from the point where the stone
hit the water waves going in every direction. Let us call this
wavelength. The trick is if you throw two stones in a pond not too far
away from each other you see the waves from the point where each stone
entered the water. But, here it comes, when those two wave reach each
other you see smaller waves. This is the trick by interfering the
wavelength of a source you can get lower wavelengts.
Beautifull
Prof. Kees