Considering a pair of sounds (e.g. [b] and [v], although any related pair will do), are they more likely to change in one direction, or are they equally likely to change in either direction? If sound change is measurably directional, which qualities tend to be more likely to survive and which ones less? E.g. is an unvoiced sound more likely to change to a voiced sound than the other way around? Or would it depend on other qualities of the sounds, so as a purely hypothetical example, perhaps [p] > [b] and [d] > [t] on average?
There probably is a directional asymmetry, but getting reliable statistical information will be a challenge. However, I seriously doubt that any sound change ever starts as a context-free change of one sound to another, instead it happens in some context, and then the context expands. Eventually you can get context-free phoneme replacements, but you can get b>p just as often as p>b – just not in the same environment.
If you focus on context-free sound changes (not the initiation of a change, but the endpoint) such as the universal replacement of Indo-European *bʰ in Greek with pʰ, then you have a classic markedness question: is it more likely that h→p or that p→h (likewise h→t vs t→h)? Ultimately, this involves a very big matrix of segment pairs and the general question, is A>B more likely than B>A. Empirically it seems that there are such asymmetries, but it is not at all obvious that we can reduce them to a single notion like "weakening" versus "strengthening", except of course if you define "weakening" as "the direction that context-free sound changes seem to prefer to go". There is a general tendency to eliminate certain kinds of contrasts, e.g. distinctive laryngeal properties, vocalic articulation on consonants, nasalization on vowels, back/round mismatches on vowels (front vowels should be unrounded, back vowels should be rounded – low vowels should not contrast frontness or backness).
There are identifiable single-property asymmetries, for example general devoicing is much more likely than general voicing, likewise general deglottalization, depalatalization. But at the same time, devoicing of just /g/ is more common than devoicing of just /b/, so for single-property changes that apply irrespective of preceding and following sounds, there can still be contextual asymmetries (the context being "other features of the segment"). A data caveat is in order, because there are generally-accepted notions of which of two kinds of sounds are "more common / basic", and that influences decisions regarding what a given sound in a language is termed. If there was a language group with a contrast [t,tʰ], and the contrast historically neutralizes in some daughter language, the chances are high that it will be reported that *tʰ→t and not that *t→tʰ. Perhaps there is a measurement basis with a comparison to VOT in a language where voiceless stops are all phonetically unaspirated, but most often language describers don't commit themselves to strong claims based on a theory of universal phonetics. My experience with Bantu is that the sounds written as p,t,k are as aspirated as they are in syllable-initial position in English and not like unaspirated stops of French or Hindi. But aspiration is usually un-noted, except when a contrast develops as in Makua, Nguni or Sotho.
To expand on Greg Lee's answer, the terms you'll probably want to search for are fortition, lenition, and sonority.
Cross-linguistically, it's common that consonants become "weaker" between vowels (lenition), and that they become "stronger" at the start of a word (fortition); the opposite is extremely rare. This is why Greg says environment matters. And it's possible to come up with an approximate ranking of the "weakness" of sounds, which linguists generally call sonority. For example, approximants are weaker/more sonorous than fricatives, which are weaker/more sonorous than voiced stops, which are weaker/more sonorous than voiceless stops.
However, it should be noted that this is more a trend or general tendency than any sort of hard rule. And it's a stronger trend in some environments than others. Fortition between vowels is extremely rare, but word-finally, fortition (e.g. in German) and lenition (e.g. in Hebrew) are both common.
For a pair of sounds related as stronger versus weaker, I don't think you can establish a direction unless you also know the environment for the change: does this environment favor fortitions (strengthenings) or lenitions (weakenings)? For instance, the beginnings of syllables or words favor fortitions, while the ends of syllables or words favor lenitions.