Не вешай нос: cheer up!
If I were really paranoid instead of just moderately deranged with a slight persecution complex, I'd say that the Russian language was out to get me. How else can you explain words whose meaning changes from weigh to hang to execute depending on a few letters in a prefix? Or one word that can mean to weigh or to execute, depending on context? Or words that flip the letters и and e to turn the meaning on its head: весить (to weigh) and висеть (to be suspended)? Ну даёшь! (For cripes' sake!)
To sort this out, let's start with the basic imperfective and transitive verb вешать. Вешать means to hang — to place something in a hanging position. Вешать шторы, пальто, бельё (to hang curtains, a coat, laundry). Картины существуют только для того, чтобы вешать их на стену. (Paintings exist only so they can be hung on the wall.) Объявления нужно вешать в каждой комнате (Notices should be posted in every room.) Одежду вешайте на спинку стула. (Hang your clothes over the back of the chair.)
Sometimes, sadly, the thing placed in a hanging position is a person. Вешали пятерых декабристов. (Five Decembrists were hanged.)
But then in colloquial speech, вешать can also mean to weigh, as in what the vendor at the market does with a hunk of cheese. Вы мне сыр вешаете? (Are you weighing that cheese for me?)
There are some handy hanging expressions. Вешать нос and вешать голову (literally to let your nose and your head hang down) means to be discouraged or dispirited. As usual, where Russian has an implied double negative — Не вешай нос! Не вешай голову! — English uses a positive: Cheer up! Keep your chin up!
I also like the expression вешать собак (to sic the dogs on someone) — to accuse or blame someone for something or everything. Ты сам виноват, а на меня вешаешь всех собак! (You did it, but you're putting all the blame on me!)
Note that a person hangs on the phone — висит — when talking for a long time, but a person hangs up the phone — вешает — when finished. Не вешай трубку! Я хочу поговорить! (Don't hang up! I want to talk!)
The perfective verb is повесить, which mostly applies to hanging. "Рабочие ещё вешают шторы?" "Нет, вчера они повесили шторы." ("Are the workers still hanging the curtains?" "No, they hung them yesterday.") Мы повесили все картины. (We hung all the paintings.)
But notice that I wrote "mostly applies." This is the nasty bit. Sometimes in colloquial speech, повесить can mean to weigh. Сколько же такой огромный судак повесит? (How much will that huge pike perch weigh?) But not always. When I'm at the market and want to know if the lemons are sold by item (поштучно) or by weight (по весу), I have a tendency to ask: Лимоны повесить? This sounds like, "Should we hang the lemons?" and makes the vendors roar with laughter.
For weighing things, it's better to use the barely pronounceable verb pair взвешивать/взвесить and the really unpronounceable command: Взвесьте мне, пожалуйста, кило лимонов. (Weigh out a kilo of lemons for me.) Weighing can be figurative, too: Взвесив все плюсы и минусы, я решила изучать русский язык. (Weighing all the pluses and minuses, I decided to study Russian.)
Well, at least I keep the vendors laughing.