hochgradig
highly
To a very high degree or extent; used as an intensifier to strengthen a quality.
Diese Chemikalie ist hochgradig giftig und muss mit Vorsicht behandelt werden.
This chemical is highly toxic and must be handled with care.

highly / severe
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highly
To a very high degree or extent; used as an intensifier to strengthen a quality.
Diese Chemikalie ist hochgradig giftig und muss mit Vorsicht behandelt werden.
This chemical is highly toxic and must be handled with care.

The word 'hochgradig' (highly/severe) is made up of 'hoch' (high) and 'Grad' (degree). Literally, it describes something that has a high degree or high level of a quality.
Das neue Material ist hochgradig feuerfest.
The new material is highly fire-resistant.
'Hochgradig' is almost always used as an adverb to intensify another adjective or participle. It stands directly before the word it intensifies.
Sein Verhalten war hochgradig unprofessionell.
His behavior was highly unprofessional.
'Hochgradig' belongs more to formal or written language. In everyday speech, people would often use 'sehr' (very), 'extrem' (extremely), or 'total' (totally) instead.
Der Plan ist mit hochgradigen Risiken verbunden.
The plan is associated with severe risks.
You can recognize the medical meaning from the context. When it is about diagnoses, illnesses, or physical limitations, 'hochgradig' usually means 'schwer' (severe) or 'stark fortgeschritten' (advanced).
Der Arzt stellte eine hochgradige Entzündung fest.
The doctor found a severe inflammation.
heavy / difficult
'schwer' and 'hochgradig' can both show that a condition is serious or strongly pronounced. 'schwer' is the more general and more common word, for example with 'eine schwere Krankheit' (a serious illness), 'eine schwere Verletzung' (a serious injury), or 'ein schwerer Fehler' (a serious mistake). 'hochgradig' means 'to a very high degree' and often sounds more technical or medical. It usually comes before qualities or diagnoses, for example 'hochgradig allergisch' (highly allergic) or 'hochgradig gefährdet' (highly at risk). 'schwer' fits many everyday situations, while 'hochgradig' sounds more precise and formal when a particularly high degree is meant.

Die Patientin ist hochgradig allergisch gegen Nüsse.
The patient is highly allergic to nuts.
Nach dem Unfall hatte der Fahrer eine schwere Verletzung am Bein.
After the accident, the driver had a serious leg injury.