The concept of medieval effigies was more than mere decoration, or even remembrance. They served an important function to those who they were built to represent, but to understand that requires a brief understanding of medieval theology.

In short; one living in Christendom during say the 13th century, could expect that only a very narrow few particularly holy members of society could be expected to enter Heaven immediately upon death. While there might be some on the other end of the spectrum with mortal sins on their soul, that could be expected to go straight to hell on death, for the the vast majority of people most would be expected to go to Purgatory for potentially thousands of years as a place to purify the soul enough to allow entry into Heaven.

This vast time could be reduced by the prayers of the living (intercessory prayer) but required both a great deal of effort (many, many prayers) as well as the praying person being able to identify the soul in purgatory. A way to accomplish this was to have a chapel built which contained the likeness of the individual whose soul the parishioners would be acting on behalf of. Thus the Effigy is an attempt to secure ones position in the afterlife, and it behooves one to have it made as lifelike to the owner as possible, so that those praying might better be able to locate the soul and see that their prayers become connected.

Given that the building of chapels and the commissioning of effigies was quite costly, they are unsurprisingly mostly a product of the affluent members of society, in particular the Knightly class began to produce effigies at a high rate in the middle of the 13th century.

For more detail on the materials used in effigies, and the implications you might read Identity, Status, and Material: Medieval Alabaster Effigies in Identity, Status, and Material: Medieval Alabaster Effigies in England England by Rachel Dressler

Dr. Tobias Capwell, the curator of arms and Armor at the Wallace Collection at London has done a series of videos on effigies which are easy to follow and very educational, collaborating with fencing instructor Matt Easton.

Capwell & Easton: Medieval knightly monumental brasses & effigies

Capwell & Easton: A medieval knightly effigy in Dennington, Suffolk - Part 1

Were these stones something the family or the dead themselves paid for or did the community chip in if the person was notable?