Question: We live in an expanding universe - so I'm told. But how can that be possible? Everything imaginable is attracted by a bigger thing. So, why can't gravitation stop the expansion of the universe? I know the "Big Bang" theory, but is it possible that the expansion of the universe is caused by the attraction of a bigger object?

Answer: 
Ok I am no professional physicist, so feel free to scrap this if you want to, but as I have had explained to me: the expansion of space is the phenomenon that distances increase, *without* relating to any motion. 

It is the space in between atoms and galaxies that gets "stretched", not that objects "move" away from each other. Like you blow a ballon up, points on the balloon get further away, but it is because of the fabric of reality itself that is expanding and not any motion of the matter in it.
I would like to start by clarifying a couple of misconceptions you have.  

1)Everything is NOT attracted to a "**bigger** thing". Everything IS attracted to **everything**.  

2)For the expansion of our universe to be caused by a "bigger thing," the thing would have to be a "shell" bigger than our universe, and the shell itself would have to be expanding as well. Therefore, this shell would also need a "bigger" shell, etc., ad infinitum (for ever).

Gravitation **could** stop the expansion. However, this is **only one of three** possible outcomes. Einstein came up with a formula that shows that if the amount of energy and matter (E & M) in the universe is more than a critical amount (CA), the universe will not only stop, but also reverse direction and start contracting (outcome 1). If the amount of (E & M) is equal to the (CA), the universe will stop expanding and **remain at the size attained** (outcome 2). If the amount of (E & M) is less than (CA), then the universe will continue to expand (outcome 3). 

At the present time, it appears that outcome 3 is the one that is going to happen, since the amount of (E & M) calculated is about 22% of the critical amount. However, if those doing the calculations did not take into consideration the (E & M) of the black holes, and the fact that the universe **is bigger** (at least twice) than the **observable universe**, this number could easily be around 90%! But because of the additional effect of "space expansion," even this larger amount won't be enough to stop the expansion.