Why does the interest rate affect higher and lower order goods disproportionately?

The answer is basically that the longer term the project is, the more interest-rate sensitive it will be…and the higher you are in the stages of production, by definition, the farther removed you are from end consumption in the production chain. This is largely described here, but just as some extra explanation,

Tom Woods in Meltdown:

The central bank’s lowering of the interest rate therefore creates a
mismatch of market forces. The coordination of production across time
is disrupted. Long-term investments that will bear fruit only in the dis-
tant future are encouraged at a time when the public has shown no letup
in its desire to consume in the present. Consumers have not chosen to
save and release resources for use in the higher stages of production.*

To the contrary, the lower interest rates encourage them to save less and thus
consume more, at a time when investors are also looking to invest more
resources. The economy is being stretched in two directions at once, and
resources are therefore being misallocated into lines that cannot be sus-
tained over the long term.

As the company works towards completing its projects, it: will find
that the resources it needs, such as labor, materials, replacement parts—
called by economists “complementary factors of production”—are not available
in sufficient quantities. The pool of real savings turns out to be
smaller than entrepreneurs anticipated, and thus the complementary fac-
tors of production they need wind up being scarcer than they expected.
The prices for these parts, labor, and other resources will therefore be
higher than entrepreneurs expected, and business costs will rise.

Firms will need to borrow more to finance these unanticipated increases in input
prices. This increased demand for borrowing will raise the interest rate.
Reality now begins to set in: some of these projects cannot be completed.
The economy is not yet wealthy enough to fund them all, although the ar-
tificially low interest rate had misled investors into thinking it was.

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  • What does it mean to say consumers “release” resources for use in the higher-
    order stages of production? Think of your income as your compensation for
    goods and services you have produced or helped produce. The less of that money
    you use to enter the economy and claim goods for your own use and the more
    of it you save, the larger is the pool of real savings from which producers can
    draw.

I highly recommend checking out some of the ABCT resources (in particular, the audio/video section and the related forum threads section for more info.)