The Western Allies (France, the US, and Great Britain, but not the USSR) wanted a strong Germany only after they started to be worried about Soviet expansionism. Before that, they wanted a weak Germany, which is why they allowed it to be split up. When the Soviets started to look like they wanted to expand their territory, the Western Allies became worried, combined their sectors of Germany, and started to try to make that country stronger (at least economically).
The Western Allies wanted a strong West Germany because they did not want Germany to become communist. If Germany became communist, they feared, the rest of Western Europe could be threatened. If West Germany had a strong economy, it would be much less likely to become a communist country. This would allow it to be an ally of the West and to act as a barrier between the Soviet Bloc and Western Europe.
The Western Allies, then, wanted a strong Germany so as to minimize the chances of communist expansion into Western Europe.