Learn English – the origin for the idiom “a hot potato”

Back in the olden days, back where there were houses made of sod on the American prairie that people actually lived in, about the time that Laura Ingalls Wilder was still Laura Ingalls, ladies used to wear dresses, men wore trousers (or pants). Also, ladies were treated as second class people. Ladies could not own property of their own. Ladies could not vote. Ladies could not enter into contracts. If you wanted to get someone in a household that had the ability to enter into a binding agreement, you needed a man. The only way you could tell a man from a woman in those days was to check to see what they were wearing. If the person was wearing pants, it was a man, and you could do serious business with him. If the person was wearing a dress, you did not bother with them.

Thus, the person in a household who makes decisions and is otherwise in charge "wears the pants".

According to phrases.org, this idiom was well known in the late 19th century. The first known appearance in print was in an November 1880 article in The Manitoba Daily Free Press where the phrase "wear the trousers" was used.

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.