to reduce the severity of (e.g. pain or grief); to alleviate (something)
to reduce or diminish (e.g. fear or suspicion)
The idea of any thing to be done in a moment, was increasing, not lessening, Mr Woodhouse's agitation. The ladies knew better how to allay it — Jane Austen
[Old English ālecgan, from a-1 + lecgan to lay]