I'm curious about how such a militaristic society (a society that used infanticide to deal with weak or "ill-born" babies) would treat the elderly. Did soldiers "retire" at a certain age, and if so, what happened to them after?
This would depend on what the cut off for "elderly" is. In certain cases, especially the more important aristocratic families, they would join the Gerousia, a very powerful political body in the Spartan government.