über ... hinweg
over / across
Expresses a duration of time or the bridging of a spatial distance.
Über die Jahre hinweg hat sich ihre Freundschaft vertieft.
Over the years, their friendship has deepened.

away / over
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over / across
Expresses a duration of time or the bridging of a spatial distance.
Über die Jahre hinweg hat sich ihre Freundschaft vertieft.
Over the years, their friendship has deepened.

The adverb consists of 'hin' (movement away from the speaker) and 'weg' (away). It is often used as a postposition or as part of a separable verb to express overcoming something or distance.
Er schaute über die Menschenmenge hinweg zum Horizont.
He looked over the crowd toward the horizon.
In its spatial or temporal meaning, 'hinweg' often appears as a postposition with 'über' and an accusative object. The structure is: 'über [etwas/jemanden] hinweg' (over/across [something/someone]).
Wir sind über die alte Brücke hinweg gefahren.
We drove over the old bridge.
The expression 'sich über etwas hinwegsetzen' means to consciously ignore a rule or a wish. Pay attention to the reflexive pronoun 'sich' and the accusative after 'über'.
Sie setzte sich über die Bedenken ihrer Eltern hinweg und reiste allein.
She disregarded her parents' concerns and traveled alone.
The expression 'jemandem über etwas hinweghelfen' means to support someone during a difficult time. The person being helped is in the dative, and the difficulty is in the accusative after 'über'.
Seine Familie half ihm über den schweren Verlust hinweg.
His family helped him through the difficult loss.
The expression 'über etwas hinwegsehen' means to intentionally ignore a mistake. What is being ignored is in the accusative after 'über'.
Der Lehrer hat über den kleinen Fehler im Test hinweggesehen.
The teacher overlooked the small mistake in the test.
over / about
'über' and 'hinweg' can both express that something bridges a distance or a period of time. 'über' is the normal preposition and comes directly before the noun, for example 'über die Straße' (across the street) or 'über den Sommer' (over the summer). 'hinweg' often appears together with 'über' in the form 'über ... hinweg'. This sounds stronger and emphasizes that something covers an entire distance or a longer period of time. For simple routes or short statements, 'über' is usually more natural. 'über ... hinweg' is more appropriate when you want to especially emphasize duration, distance, or a development.

Über viele Jahre hinweg hat Maria ihre Freundin regelmäßig angerufen.
Over many years, Maria called her friend regularly.
Die Kinder laufen über die kleine Brücke zum Spielplatz.
The children run across the small bridge to the playground.