A list of “large & small” words from around 1968 had pia “little” derived from √PEYE (PE17/115), probably from primitive *peya with eya > ia. This was followed by words pikina, pinke, and pitya, all probably derived from a different root ᴹ√PIK (Ety/PIK).

Neo-Quenya: I think the root √PEY was probably a transient idea, quickly reverted back to √PIK. For purposes of Neo-Quenya I prefer other words over pia “little”.