It appears 552.221(b)(2), Gov't Code would permit you to await payment of the accrued fees before sending out the copies of public information. And 552.261(d) says the charges accrue before delivery and talks about the copy being available on payment. But then 552.263 seems to limit the need for advance payment to certain situations (i.e., where more than $50 accrues). My question arises because I have an inmate who states in his request "I'm indigent and can't pay any fees." Must this type of request be honored? I expect the charge for what he has requested will not be more than $25 or so.

You have a few options here.

You don't have to send out freebie copies under the PIA to anyone, even on a claim of indigency, but you can choose to do so if you feel it is in the public interest. Your call.

Or, the Texas Government Code says you don't even have to respond to inmate requests(though, if you have already been corresponding with him about this, you may want to send him a copy of this law):

Sec. 552.028. REQUEST FOR INFORMATION FROM INCARCERATED
INDIVIDUAL. (a) A governmental body is not required to accept or
comply with a request for information from:
(1) an individual who is imprisoned or confined in a
correctional facility; or
(2) an agent of that individual, other than that
individual's attorney when the attorney is requesting information
that is subject to disclosure under this chapter.
(b) This section does not prohibit a governmental body from
disclosing to an individual described by Subsection (a)(1), or that
individual's agent, information held by the governmental body
pertaining to that individual.
(c) In this section, "correctional facility" means:
(1) a secure correctional facility, as defined by
Section 1.07, Penal Code;
(2) a secure correctional facility and a secure
detention facility, as defined by Section 51.02, Family Code; and
(3) a place designated by the law of this state,
another state, or the federal government for the confinement of a
person arrested for, charged with, or convicted of a criminal
offense.