
weithin
far and wide
Across a great spatial distance or over a large area; visible or spread far and wide.
Der Leuchtturm ist bei klarem Wetter weithin zu sehen.
The lighthouse can be seen far and wide in clear weather.
far and wide / widely
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far and wide
Across a great spatial distance or over a large area; visible or spread far and wide.
Der Leuchtturm ist bei klarem Wetter weithin zu sehen.
The lighthouse can be seen far and wide in clear weather.

widely
To a high degree or among most people; largely, generally.
Es ist weithin bekannt, dass Rauchen der Gesundheit schadet.
It is widely known that smoking is harmful to health.
The adverb 'weithin' (far and wide/widely) is a compound of 'weit' (far) and 'hin' (toward/there). It describes an extent or effect that stretches over a great distance ('weit') in a direction ('hin').
Das Feuer war weithin zu riechen.
The fire could be smelled far and wide.
The meaning of 'weithin' (far and wide/widely) depends on the context. In combination with verbs of perception such as 'sehen' (to see) or 'hören' (to hear), it means spatially 'over a great distance.' In combination with words like 'bekannt' (known) or 'anerkannt' (recognized), it means figuratively 'generally' or 'among many people.'
Die Ruine auf dem Berg ist weithin sichtbar. (räumlich)
The ruins on the mountain are visible far and wide. (spatial)
In its spatial meaning, 'weithin' (far and wide) is often combined with adjectives or participles that describe sensory perception. Common collocations are 'weithin sichtbar' (visible far and wide), 'weithin hörbar' (audible far and wide), or 'weithin zu sehen' (to be seen far and wide).
Der Jubel der Fans war im ganzen Tal weithin hörbar.
The fans' cheering was audible far and wide throughout the valley.
In its figurative meaning, 'weithin' (widely) describes the degree to which information or an opinion is widespread. Typical combinations are 'weithin bekannt' (widely known), 'weithin verbreitet' (widespread), and 'weithin akzeptiert' (widely accepted).
Die Ansicht, dass Bildung wichtig ist, ist weithin verbreitet.
The view that education is important is widespread.
largely
Weitgehend describes the high degree to which a statement applies or something is accepted. Weithin focuses more on general prevalence, for example among many people. Weitgehend is appropriate for almost complete agreement within a group, while weithin is appropriate for broad social acceptance.

Die neue Regelung ist in der Bevölkerung weithin akzeptiert.
The new regulation is widely accepted by the public.
Die Fachleute akzeptieren die neue Regelung weitgehend, kritisieren aber ein Detail.
The experts largely accept the new regulation, but they criticize one detail.