eng
narrow / tight
Offering little space or room; not wide or spacious.
Die Straße ist zu eng für zwei Autos nebeneinander.
The road is too narrow for two cars side by side.

narrow / close / tight
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narrow / tight
Offering little space or room; not wide or spacious.
Die Straße ist zu eng für zwei Autos nebeneinander.
The road is too narrow for two cars side by side.

'Eng' (narrow/close/tight) can also be used as an adverb to describe the way an action is done. It then means 'close together' or 'intensively'.
Die beiden Abteilungen arbeiten bei diesem Projekt eng zusammen.
The two departments are working closely together on this project.
To describe a close relationship, 'eng' (close) is often combined with people or relationships. Typical phrases are 'ein enger Freund' (a close friend), 'eine enge Beziehung' (a close relationship), or 'enge Familienbande' (close family ties).
Er ist einer meiner engsten Freunde seit der Schulzeit.
He has been one of my closest friends since school.
When it comes to limitations, 'eng' (tight) is often used for abstract things like time or finances. Common combinations are 'ein enger Zeitplan' (a tight schedule), 'ein enges Budget' (a tight budget), or 'in die engere Wahl kommen' (to be shortlisted).
Wegen des engen Budgets können wir dieses Jahr nicht in den Urlaub fahren.
Because of the tight budget, we can't go on vacation this year.
The expression 'in engem Kontakt stehen' (to be in close contact) is often used with the preposition 'mit' followed by the dative to name the person or group one is in contact with.
Ich stehe in engem Kontakt mit meinem ehemaligen Professor.
I am in close contact with my former professor.
far / wide
'weit' and 'eng' both describe how much space there is, especially with clothing, rooms, or paths. Here they mean the opposite. 'weit' means that something fits loosely or offers a lot of space. 'eng' means that there is little space or that something fits tightly. With clothing, the difference is especially clear: 'eine weite Hose' (loose pants) leaves a lot of room, while 'eine enge Hose' (tight pants) fits close to the body. A room can also feel 'weit' or 'eng'.

Nach der Arbeit sitzen die Gäste in der engen Küche zusammen.
After work, the guests sit together in the cramped kitchen.
Laura trägt im Büro gern weite Jacken, weil sie bequem sind.
Laura likes wearing loose jackets at the office because they are comfortable.