so that / with it
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so that
As a conjunction, introduces a subordinate clause that describes the purpose, goal, or intention of the action in the main clause.
Er spricht lauter, damit ihn alle verstehen können.
He speaks louder so that everyone can understand him.
You can recognize the difference by the sentence structure: As a conjunction, 'damit' (so that) introduces a whole subordinate clause whose verb comes at the end. As an adverb, 'damit' (with it/with that) stands on its own and refers to a thing; if it comes at the beginning of the sentence, the verb follows directly.
Ich beeile mich, damit wir den Zug nicht verpassen. (Konjunktion)
I'm hurrying so that we don't miss the train. (conjunction)
As a conjunction, 'damit' (so that) describes a goal or purpose. One important feature is that the subject in the main clause and in the subordinate clause can be different.
Die Eltern sparen Geld, damit ihre Kinder später studieren können.
The parents are saving money so that their children can study later.
As a pronominal adverb, 'damit' (with it/with that) is a compound of 'da' and 'mit'. It literally means 'with that' or 'with this thing' and replaces a previously mentioned thing to avoid repetition.
Ich habe ein neues Programm installiert. Damit arbeite ich viel schneller.
I installed a new program. I work much faster with it.
because
'weil' and 'damit' both introduce subordinate clauses, but they answer different questions. 'weil' explains the reason: Why does something happen? 'damit' explains the goal or intention: What is someone doing something for? They can seem similar because both clauses contain an explanation. But the difference is important. If something is already the reason, 'weil' fits. If someone does something so that something can be achieved later, 'damit' fits.
Sie erklärt die Aufgabe langsam, damit alle Schüler sie verstehen.
She explains the task slowly so that all the students understand it.
Die Fahrerin hält an, weil ein Kind über die Straße läuft.
The driver stops because a child is crossing the street.