The origin of this type is discussed in the above book by Burrow, but I'd explain it in Latin terms.
Many Proto-Indo-European nominals showed vowel alternations in the declension, in particular the nominative singular often possessed a lengthened grade: a pattern that survives (although modified) in the Latin
pēs — pedis.
With time, this alternation tended to disappear, with either form generalized across the paradigm: for example
rēx — *reges (from Proto-Indo-European
*Hrēgʲs — *Hregʲ-) was replaced with
rēx — rēgis. The relational adjective from this noun inherited the long vowel:
rēgius.
From
pēs — pedis, however, the attested adjective is
-pedius (e. g.
acūpedius).
Imagine that both variants of relational adjectives once existed, that is
*regios/*pedios and
*rēgios/*pēdios. If by some chance the noun generalized the full grade (
**rex, **pes) while the adjectives still survived in both variants, we would get the situation described by Burrow for earlier Indic, where both full- and lengthened grade- derivatives are sometimes attested. At the next stage, the pattern
**rex — rēgius started to expand, which has resulted in the system so characteristic of Sanskrit.