Strings for these instruments were, historically, made from sheep gut or cow gut. In some situations it wouldn't be possible to make a thicker lower string, so a higher-octave string is substituted. In other situations there would be a point at which it isn't possible to make a thinner string that could be tuned higher. Such a string would be too weak and would break just from tuning it up to pitch. So the solution was to use a string tuned an octave lower in its place.
Reentrant tunings and strings have been used as long as there have been stringed instruments that were used to strum chords. That would take us at least back to the early 1600s with the appearance of the Baroque guitar.
The ukulele only dates from the 1880s, but it is descended from the Portuguese guitar (brought to Hawaii by Portuguese traders and colonizers) which is, in turn, descended from the Baroque guitar. The Baroque guitar used a reentrant tuning from its inception around 1646. Before that there was the lute, going back to antiquity, and also using reentrant tunings.
So one reason that the ukulele has a reentrant tuning is that it comes from a continuous line of reentrant-tuned instruments going back hundreds of years before the invention of the ukulele.