stregth of armies overtime?

As you begin to take a country does their army slowly become weaker? Which allows you to take the regions faster, instead of taking half a year maybe take a few weeks if done correctly?

Not really. If a faction lose a region (I suppose you are speaking about France or a large faction with several region), you will reduce their income a little, so their capability to maintain a large army, and you will also reduce the number of regions where they can recruit units simultaneously.
This will reduce their capability to field large army.
However, the capitale region (France or England for instance) are where the main buildings are located, and the region generating most income.
Just to give an example, taking Wales will reduce Britain capability by perhaps 10%, while taking England will reduce it by 70%.

Don't forget also that if you wait, they can improve their building/roads, and so get more income, and can also get access to more types of units, and better units.

What is also important is to raid their ports and sea trade routes to reduce the income from trade.

I see, when I took Spain it became easier, after taking Madrid, to take the whole country.