The Phrase finder provides an explanation of the origin:
: To be under the weather is to be unwell. This comes again from a maritime source. In the old days, when a sailor was unwell, he was sent down below to help his recovery, under the deck and away from the weather.
... Here's a similar one I found: "Under the weather. To feel ill. Originally it meant to feel seasick or to be adversely affected by bad weather. The term is correctly 'under the weather bow' which is a gloomy prospect; the weather bow is the side upon which all the rotten weather is blowing." From "Salty Dog Talk: The Nautical Origins of Everyday Expressions" by Bill Beavis and Richard G. McCloskey (Sheridan House, Dobbs Ferry, N.Y., 1995. First published in Great Britain, 1983).
Another site states that something similar:
Passengers aboard ships become seasick most frequently during times of rough seas and bad weather. Seasickness is caused by the constant rocking motion of the ship. Sick passengers go below deck, which provides shelter from the weather, but just as importantly the sway is not as great below deck, low on the ship.
In both cases, we have two things in common. One, is its origin came from sea travel, when people felt ill due to several reasons, and the other thing in common, is that they both cited the fact that the persons feeling unwell went below deck.
The word operator has had several slang meanings over time, according to the Oxford English Dictionary. A brief list of the time and definition of operator is:
1598: A person who performs a surgical operation or operations; an operating surgeon or dentist.
1611: A person who deals in quack medicines, etc. Obs.
1704: A person who commits fraudulent operations; a thief, a pickpocket.
1828: A person who carries on (speculative) financial operations. Also: a person adept at speculative or shrewd operations; (formerly) a person who acts in a cunning or underhand manner.
1838: A person who or company which runs a business, enterprise, etc.
1944: A person with a talent for seduction; a smooth talker.
The phrase smooth operator starts to appear in the late 1890s. For example, in "The Strange Schemes of Randolph Mason", it says:
Here, a smooth operator is someone who is "smooth" at running a business or set of financial operations (the senses from the earlier 1800s). This is not the only application of smooth operator. In the 1980s, the OED notes the following usage:
1980 Photo-Love Summer Spectacular 7/1 You're quite a smooth operator, what with names and telephone numbers just like that!
The "operation" has changed over time. In the 1700 and 1800s, the "operation" was financial--it referred to either theft operations, speculating on stocks (operate as a verb meant "To deal or speculate in stocks or shares; to buy and sell commodities as a broker"), or business operations. Then, in the 1900s, the "operations" referred to the "business" of playing at courtship and seducing women.
Thus, now a smooth operator can refer to the "business" of financial operations or seduction operations, with smooth modifying operator in a primarily (and possibly solely) negative way.
Best Answer
The OED’s first citation for ‘let her rip’ is dated 1840. In this sense, the dictionary describes it as colloquial and originally of US origin. It is defined as ‘an exhortation not to restrict the speed of something; (hence) an invitation to act without restraint or to pursue a reckless course’.