Learn Dutch: Ten gevolge van de besmetting werd de man steeds zwakker. - As a result of the infection, the man became steadily weaker.

It is highly formal and often used in medical, legal, or news contexts. It literally means 'to the consequence of', containing an old, frozen grammar form of the word gevolg (consequence). In everyday speech, you would usually just say door (because of) instead.

Why does the verb werd come before the subject de man?

This is a classic example of inversion caused by the V2 (verb-second) rule. The sentence starts with a long prepositional phrase (Ten gevolge van de besmetting). Because that whole phrase occupies the first position, the verb (werd) must take the second position, pushing the subject (de man) right after it.

I learned that steeds means 'always' or 'still'. Why does it mean 'steadily' here?

When you pair steeds with a comparative adjective like zwakker (weaker), the meaning changes to 'increasingly' or '[adjective] and [adjective]'. So steeds zwakker translates to 'steadily weaker' or 'weaker and weaker', showing an ongoing, progressive change.

Could I use the other formal preposition from this lesson, naar aanleiding van, here instead?

No, because their exact meanings differ. Naar aanleiding van means 'in response to', which implies a human reaction or action (like starting an investigation in response to a tip). Ten gevolge van strictly means 'as a direct result of', which perfectly describes an infection physically causing weakness.