Why is a cross † used as footnote marker for people?

The dagger, which sometimes looks like a cross, has long been used to as a foot- or sidenote. Here's an example from 1582, though the practice is much older than this:

Here's a link to the page on Google Books

As you can see, the dagger is used (here) at a "secondary level" from the main set of glosses, which used suprascript letters. The dagger in this case is to the note on the far right by the editors of this edition of the book to make a comment about different readings for the word Bononiae (= Bologna).

It is not a cross, it is a dagger. It is used for footnotes if an asterisk has already been used. See also: https://en.wikipedia.org/wiki/Note_(typography)

The cross mentioned is not really a cross, essential a cross-looking symbol. It is more precisely, or more generally, called the dagger symbol (\dagger in LaTeX).

It appears as a variant of the obelus (same root as a pointy obelisk), a symbol apparently invented and used by Greek scholars (potentially by Zenodotus or Aristarchus), with many sword-shaped variations:

It was used to mark corrupted, doubtful, interpolated or spurious texts, or even superfluous passages in ancient manuscripts (initially, Homeric epics). Other variants are depicted below, from Characters from the Margins of Ancient Texts:

Asterisks and Obeli: Categories of Usage provides many examples and details, such as in the following picture:

It is composed of an horizontal bar, accompanied by two dots, one above and one below. Its uses and interpretations have varied along time. For instance, the sign has been occasionally used as a subtraction sign in mathematics. It was first used for division by mathematician Johann Rahn in 1659.

It is called dagger or obelisk equally in Henry Beadnell, A guide to typography: In two parts, literary and practical, 1859.

The word obelos (ὀβελός) in Greek stands for "spit roast" or "roasting jack". It was meant to roast meat devoted to Gods. Obelisk is its diminutive form (small "obelos"). It may originate from belos (βελός), the Greek for arrow, dart, missile.

There is thus a strange weaponry connection (between the dagger and the arrow) behind this typographic sign.