We visit family in Weymouth regularly and there's lots to do!
My DS (nearly 6) likes scooting along the seafront (which from Overcombe corner to the pavilion is over a mile each way). The Oasis cafe at Overcombe corner is nice to stop at for a snack. Once at the far end, you can pay to go up the Sea Life tower which gives good views over the bay.
There's a Sea Life Centre on the Preston Beach road which also has some mini-golf type things at it which would be popular with older DC.
The Nothe Fort is good for a visit - you can do various trails, dressing up and hunting around dungeons, etc.
The isle of Portland has some good stuff: you can climb the Portland Bill lighthouse. The Lobster Pot cafe at the bottom is nice, or there's the Jail house cafe which is actually part of the prison (but not as scary as it sounds!)
We like going to Abbotsbury (village about 9 miles west of Weymouth) where there is a Swannery and lovely SubTropical gardens. Plenty of nice cafes here and pubs for lunch. You can also climb a hill up to St Catherine's Chapel which has a lovely view.
On Saturdays there's Bridport Market (another 9 miles past Abbotsbury, so about 18 miles out of Weymouth) which has lots of good toy stalls so is popular with DC.
Dorchester (just a few miles north of Weymouth) has a dinosaur museum and (I think) a Tutenkhamun museum. It also has the county museum which is interesting in parts. If you're a fan of Thomas Hardy novels, there's lots of walks you can do as his stories are all set in that area.
Near Dorch is Kingston Maurwood which is an agricultural college that has a children's petting zoo type thing and various walks and cafes in the grounds that we like. There's also Poundbury which is Prince Charles' village project and looks quaint to walk around. Lots of nice cafes and playgrounds which little DC would like. Also a chocolate factory!
The main beach in Weymouth is also really nice: lots of rides, Punch and Judy, traditional stuff like that.
Hope you have a lovely time!