> e.g. exoplanets based on minute wobbles and brightness variations, water on said exoplanets based on spectrography.
The minute wobbles may be tiny, but they can plot a curve of those wobbles and see very clearly that it changes in a certain way that can only be caused by a planet (or something spherical and with a certain mass). If there was a competing theory of how you can get this exact curve in some other way, I am sure we would consider them as alternative possibilities and not be able to tell them apart, but as far as I know, there isn't any competing theories at all... so we can have very high confidence there's a planet there.
Regarding water detection: yeah, spectrography is just mind blowing, but again, given what we know, there's just nothing that could justify believing that when you detect radiation that fit exactly what you would expect from water molecules, that it could be something else instead... unless you come up with a convincing "something else", your only option is to conclude that the detection is accurate, otherwise you would need to stay open to the possibility of absolutely everything possibly having alternative explanations we haven't thought of yet (though every now and then, that indeed can happen and we need to adjust all our theories that are based on the changed body of knowledge), and progress would not be possible in any area (you need to accept something before you can build on top of it).