To add to the comments above:
AFAIK freewheel cogs can't have less than 13T, while cassettes can go down to 11T.
Unless you have quality rim/spokes at present it might be false economy to have them rebuilt with a new hub. Wheels are often sold for less than the sum of their parts and rebuild labour cost.
If your existing wheel has a 7 speed freewheel, depending on its vintage your frame "might" have a distance between rear dropouts of 126mm. Generally modern road freehubs are 130mm and mtb freehubs are 135mm so worth checking. Steel frames (unless they are exotic ones) can usually be spread without problem, but alloy frames should not be spread by very much at all.
Assuming it is Shimano, a (4.5mm iirc) spacer is needed between a 7 speed cassette and a modern 8/9 speed freehub.
Freewheel/hubs are usually heavier whether they have solid spindles or otherwise. Casette/Freehubs are generally lighter and most come with hollow spindle and quick release.