weit
far
Describing a large spatial distance or extent.
Von hier bis zum nächsten Dorf ist es ein weiter Weg.
From here to the next village, it's a long way.

far / wide
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far
Describing a large spatial distance or extent.
Von hier bis zum nächsten Dorf ist es ein weiter Weg.
From here to the next village, it's a long way.

To ask about a distance, you use the fixed question construction 'Wie weit ist es ...?' (How far is it ...?). The prepositions 'von' (from) and 'bis' (to/until) or 'nach' (to) help define the starting and ending point.
Wie weit ist es von hier bis zum Bahnhof?
How far is it from here to the train station?
In reference to clothing, 'weit' (wide/loose) means the opposite of 'eng' (tight). It describes that a piece of clothing fits loosely and offers a lot of freedom of movement.
Im Sommer trage ich gerne weite Kleider.
In summer, I like wearing loose dresses.
As an adverb, 'weit' can stand before a comparative (e.g., better, bigger, faster) to emphasize the difference. It then means 'much' or 'significantly'.
Ein E-Book ist oft weit günstiger als ein gedrucktes Buch.
An e-book is often much cheaper than a printed book.
The idiom 'zu weit gehen' (to go too far) means to cross a social, moral, or personal boundary. It expresses that a behavior is no longer acceptable.
Seine Witze waren nicht mehr lustig, damit ist er zu weit gegangen.
His jokes weren't funny anymore; with that, he went too far.
The expression 'bei weitem' (by far) is used to emphasize a large difference. It often appears in connection with a comparative or superlative and means 'by a wide margin'.
Das war bei weitem der schwierigste Test, den wir je hatten.
That was by far the most difficult test we have ever had.
The expression 'so weit' (so far) is used to ask about the state of things or to describe an interim status. It means 'up to now' or 'in general'.
So weit ist alles gut gelaufen mit dem Projekt.
So far, everything has gone well with the project.
much / a lot
'viel' and 'weit' can seem similar in comparisons because both can intensify a large difference. For example, you can say that something is 'viel besser' or 'weit besser' (much / far better). 'viel' is very normal and everyday in this use. 'weit' often sounds a little stronger or more formal in such comparisons and fits especially well when you want to emphasize a clear gap. They can be confused because both can come before a comparative. Outside such comparisons, however, they are different: 'viel' talks about quantity or frequency, while 'weit' usually talks about distance or extent.

Nach dem Training läuft Max weit schneller als früher.
After the training, Max runs far faster than before.
Mit der neuen Brille kann ich viel besser lesen.
With the new glasses, I can read much better.