Nothing hidden in this word. However, I noticed today that it’s related to the word väljas (outside), so I decided to find out more declensions of this word and see where that would lead me. This is what I found out. Bear in mind, as I am no linguist or anything close, just curious by nature.
välja is the genitive case, which means “of the field”. This is the Estonian word for out.
väljas is the innesive case, so this would be mean something like “in the place of the field“. This actually means outside or afield.
väljast is the elative case, which is like “out of the field“. This in Estonian actually means “from the outside“. The word outsourcing in Estonian is related to this (väljasttellimine, literally “order from the outside“).
väljal is the adessive case, which would be “on the field“. Just think of a person standing on a field.
väljalt is the ablative case, which is something like “off the field“. Imagine when someone picks a flower off a field.
Although it might not be related, I wonder if väljak (square, the place, not the shape) is related to this too.
My brain is tired now.