The spec on those bikes was very much low-end. You may very well find replacing the rear derailleur with a better one will do the trick.
Do bear in mind that 7-speed shifters (if that's what's fitted) do not agree with 6-speed gears (again, if that's what's fitted), even if mtuned to lock out the extra shift point. 6-speed has slightly wider sprocket spacing, so the indexing of 7-sp. does not match. On the other hand, 8-sp. shifters do work perfectly well on 7-sp. systems as the spacing is the same.
Just ride the bloody thing and enjoy yourself!