Shoogi-boo.........If your mobile home is not on a slab then you should be concerned. If you have access to the underneath I would take meaurements of where the tank is set-up and then check to see what support you have at it's location beneath. To say you have nothing to worry about is wrong. About 1000-1200 pounds in a about a two foot by four foot area is alot of weight. Over time your stucture could be compromised and the tank could fall through the floor. Naturally, this would most likely not happen when the tank is first set-up, but can happen over a period of months and/or years. Especially if it is running perpendicular to your joists and not set-up by a load bearing wall. ...if you have a wood type construction for a foundation.
Do some serches on the internet and you will find advice as to how a tank should be placed on a wood type foundation and why.