Profound being an adjective, is its usage in the sentence below correct?
Loneliness is profound on weekends.
Yes........in the sense of "deeply felt" or "severe"
Yes, though it should be noted that this is saying that it is generally true (that loneliness is intense on weekends for everyone or a majority of the population) rather than specifically true (someone being intensely lonely during weekends). If you wanted to say the later, you would say "I am profoundly lonely on the weekends" or "My loneliness is profound on the weekends."