The last century of the Roman Republic was filled with civil wars, especially the last few decades that heralded the fall of the republic, did this leave the fledging roman empire under octavian really weak? Why didnt Rome face contractions in territory due to bleeding itself dry?

Not particularly. 

Augustus had the advantage of being personally incredibly wealthy, combining his inheritance from Julius Caesar with what he gained from the proscriptions of the assassins and his plundering of Egypt. He then added to that by sweeping reforms of Rome’s taxation system, shifting from a system of provincial tax farming to direct taxation based on population censuses and carried out by civil servants, which increased and stabilized Rome’s revenues enormously.

And Augustus was able to turn that wealth towards shoring up the capacity of the state in everything from expanding the bureaucracy to massive public works, to expanding the empire…which helped him deal with the enormous number of men under arms by the end of the civil war (the Battle of Phillipi saw as many as 410,000 participating):

The yellow represents the Roman Empire at the time of Augustus’ accession, the greens represent conquests made in his reign, and the pink represents kingdoms which became clients/allies of Rome during his reign. However, Augustus was always careful to avoid conflicts with Parthia, the only power that could rival that of Rome. 

Towards the end of his reign, Augustus started running into problems of over-extension – notably his defeat at Teutoberg Forest – and had to abandon his ambition of conquering Germany in favor of holding the Rhine/Danube border and “pacifying” the German tribes through a combination of military raids and bribing client kings so as to divide and conquer the tribes of Germania.