If you look at the definition of since in the Cambridge dictionary, it says
from a particular time in the past until a later time, or until now
"from a particular time" must be something like "july" or "2009" or "4pm".
If you want to specify a time interval, like a week or an hour, you have to use for.
for weeks is a prepositional phrase, and we normally put prepositional phrases after the sentence. Also, you use past perfect had been waiting if he was waiting until some time in the past. If he has been waiting until now, you should use present perfect has been waiting:
He has been waiting for the reply for weeks.
Prepositional phrases are a special kind of adverbial, and you are allowed to move adverbials to the start of a sentence, followed by a comma:
For weeks, he has been waiting for the reply. -unusual
This places an emphasis on the adverbial: in my opinion, the emphasis is not appropriate for this sentence, so placing the prepositional phrase at the end sounds better.