Hi,
I have a table that is going very slow. The table has four indexes, three non clusterd.

EXEC sp_spaceused 'Tablename'

Yields something interesting...

The data size is pretty big: 2.5 Gig

But the index size is even bigger: 3.3 Gig.

I'm not a DBA but if the index size is bigger than the data size - this doesn't too good. Is this reasonable assumption?

And what would be example of how an index can end up goggbling memory?

Not necessarily.

The indexes could be highly fragmented, or the keys themselves could be very big. Try rebuilding the indexes, and see if that relieves any of the slowness. Remember to quantify what "slowness" means now, before you start trying things, so you can tell if you were at all successful.