It's very well known that Wittgenstein thought that with the Tractatus the problems in philosophy were pseudo-problems, but then went on to produce further philosophical works like The Philosophical Investigations. I've read the former, but not the latter. What were his later opinions on philosophy? In particular, did he think that metaphysical questions could be answered? Why did he change his mind? Specifically, how did that side of Wittgenstein's thought evolve?
I believe what you are looking for is the notion that Wittgenstein went from thinking objectively to intersubjectively about language. According to Borchert's entry, where the original Wittgenstein believed strongly in notions that propositions were a "logical form of reality" with his belief sentences were "psychological constituents" which made them a literal "picture" as fact of which the facts were "atomic" and formed the basis of axiomatic reasoning (See Agrippan trilemma) and corresponded to the "state of affairs", he moved, in Philosophical Investigations, to meaning as it came from a game played between persons in which usage was the primary determinant of meaning and began to recognize through observations about the definition of 'game'; that there were means of definition that went beyond necessity and sufficiency, and termed them "family resemblances" which anticipated prototypes in cognitive science.
Why change? Well, that's a complicated issue (some write books on it), but it boils down to the idea Wittgenstein's metaphysics changed as it admitted new phenomena into his ontological commitment and epistemic attitude! If one concedes that Wittgenstein started and developed a correspondent theory of truth, it is plain that ultimately he landed in a much more pragmatic theory, and he moved away from "logical compulsion", that is rejecting deduction as a primary mode of reasoning moving towards inferential and abductive modes. Meaning no longer came from names which corresponded with facts, but elsewhere, such as the language game. "In your act of meaning or understanding, 'your mind as it were flew ahead and took all the steps' before they were taken physically (*Investigations, Sec. 188)" [P.813]. On page 814, the encyclopedia says, "[Wittgentstein] held that the way a rule is applied in particular cases determines its meaning."
In other words, he went from truth and meaning grounded in an objective reality to which our thoughts were mere correspondence, to a position that truth and meaning itself became a reflection of the intentionality of the person using it. In a way, doesn't our metaphysical development generally follow that thinking, a path starting with subjectivism, moving on to a better theory of meaning and truth derived from objectivity, to an ultimate understanding that objectivity itself is just a tacit agreement of subjective parties?
Here's a comic I came across which makes the point in painted panes. Existential Comics: Wittgenstein's Monster
Anat Biletzski and Anat Matar describe the change in terms of "dogmatism":
The complex edifice of the Tractatus is built on the assumption that the task of logical analysis was to discover the elementary propositions, whose form was not yet known. What marks the transition from early to later Wittgenstein can be summed up as the total rejection of dogmatism, i.e., as the working out of all the consequences of this rejection. The move from the realm of logic to that of ordinary language as the center of the philosopher’s attention; from an emphasis on definition and analysis to ‘family resemblance’ and ‘language-games’; and from systematic philosophical writing to an aphoristic style—all have to do with this transition towards anti-dogmatism in its extreme.
They also note at the beginning of their article that there is a difference of opinion on how significant this change actually was:
Originally, there were two commonly recognized stages of Wittgenstein’s thought—the early and the later—both of which were taken to be pivotal in their respective periods. In more recent scholarship, this division has been questioned: some interpreters have claimed a unity between all stages of his thought, while others talk of a more nuanced division, adding stages such as the middle Wittgenstein and the third Wittgenstein.
One might use the idea of dogmatism when trying to identify differences between these two periods keeping in mind that the difference may not be as great as imagined.
Biletzki, Anat and Matar, Anat, "Ludwig Wittgenstein", The Stanford Encyclopedia of Philosophy (Summer 2018 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/sum2018/entries/wittgenstein/.