A few of the notes in Weber Piano Quartet in Bb Major Op. 8 movement 1 have two accidentals in front of them. For example, in one of the measures a Bb has a sharp and a natural accidental in front of it. Does this mean that the accidentals cancel each other out and the note remains as written in the key, Bb?
At this period a single accidental, following a double, was often written with a natural sign before the accidental to "cancel" the first of the double accidentals.
The Weber example is a bit odd, because B# is conceptually a "double sharp" relative to the key signature Bb (i.e. it raises the pitch by two semitones) even though the notation only contains one essential symbol (the sharp) not two.
The notation might have been more logical if Weber had changed the key signature and finished the modulations in C# major instead of Db - but he didn't.
(Score and parts at https://imslp.org/wiki/Special:ImagefromIndex/66084/torat – but since this PDF is intended to be printed out and then folded as a set of booklets, one for each part, beware that the page order in the PDF itself is seriously weird!!)
This is typically done when a double sharp is lowered back to just a sharp. In certain melodic minor scales, you find this also. a# minor has a Gx for a Leading Tone (When the scale ascends) and when you have the descending natural minor form that Gx is lowered back to a G#.
There is also the other way of notating this phenomenon. I suspect the American tradition just uses a sharp and not use the natural sign, but I was taught that the use of the natural sign and then the sharp is typical.
The B in that bar is originally (in that key) Bb. The note in question is followed by C#. I believe the natural sign is to firstly make that Bb into a B, then the sharp makes it into B#, probably the leading note into C#. That Bb has to be naturalised first? Not sure, as any accidental is effective on the note it precedes, so just a sharp sign would probably suffice. However, that may appear as a potential mistake to the reader, so it's sort of a courtesy sign.
You're right, this is a slightly awkward notation.
In general, cautionary accidentals are good practice, but they should be used to clarify the effect of a preceding accidental on a repeated note, not the interaction of an accidental with a key signature (Elaine Gould, Behind Bars p.81).
In this context the meaning of "natural/sharp/b" is definitely "play b sharp", and presumably the editor did try to clarify the meaning by including the natural; however, this is not necessary and in fact confusing, since a sharp directly in front of a note cannot mean anything else.