Is it possible to make a weak analog low-pass filter with less than 20 dB/decade roll-off?
Yes it is but it's more complex because you have to use breakpoints formed by a multiple array of resistors and capacitors:



The above is a piecemeal 3dB per octave (10 dB per decade) filter. It was designed to convert white noise to pink noise. See this link.

Here's another white to pink noise filter using an op-amp with a few more breakpoints:



You could convert it to 2 dB per octave or 4 dB per octave but the accuracy comes from the number of breakpoints and therefore the number of RCR stages.

Note that pink noise rolls off at 3 dB per octave and here's the final "circuit" and graph: