Elimination reactions - basic question

[reising1]

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There is a famous reaction as so:
Alkene + H2O <=> Alcohol

Concentrated acid and heat causes it to shift left.
Dilute acid and cold causes it to shift right.

But why is this? I thought that in elimination reactions, when double bonds are formed, bases are used. So I would think a weak acid would promote the production of the alkene, the double bond.

What's wrong here in my logic?

 

[FuzzyMemory]

This is a classic dehydration/hydration equilibrium reaction between an alkene and an alcohol. Concentrated acid is required because it protonates the hydroxyl group, allowing it to act as the leaving group in an E2 elimination reaction, forming an alkene from an alcohol.

I suggest reading this link, as it explains it quite well:
http://chemwiki.ucdavis.edu/Organic..._by_Dehydration_of_Alcohols#Alcohol_as_a_Base