I wouldn't advise travelling via Castle Cary if time is tight - the Exeter stoppers and Weymouth trains are both 2 hourly and connections are often sub-optimal. If you do miss a connection, the town's some way off and there's not much around the station.
Weymouth has plenty of nice spots even if the area around the station is sufficiently grim it's led to the permanent closure of the station toilets. The beachfront along the Esplanade is very nice and has fine views over towards Ringstead Bay and Lulworth Cove (although not into the Cove). Brewer's Quay is very pleasant, as is the Nothe Gardens overlooking Portland. There's also the Rodwell Trail on the old railway route to Portland which has some fine views south of Sandsfoot Castle over Weymouth Bay. Admittedly none of these are very close to the station and if you aren't a keen walker, may not be doable without a taxi.
Poole does have a very long beachfront - but it's so far off it makes Bournemouth station look close to the beach. It's about an hour's walk from Poole or Parkstone stations to Sandbanks / Shore Road beach, and about 45 minutes at a brisk pace from Branksome to Branksome beach. Bournemouth is the best of a poor bunch - Pokesdown and Christchurch aren't much better. New Milton is about a brisk 40 minute walk from the beach at Barton on Sea.
All beaches mentioned are sandy if that helps.
The London - Weymouth route is quite nice - the only place you can have a 100mph run these days on the third rail as far as Winchester IIRC. Rolling chalk hills through Hampshire, impressive views of the Itchen and Test at Southampton, a pleasant run through the New Forest, views of Poole Harbour either side of Poole, a run beside the Frome over the Dorset heathland, then finally a climb past Maiden Castle south of Dorchester before dropping down into Weymouth as the sea comes into view. Granted it isn't the West Highland but it's quite varied and largely rural.
Still a very long day out though, particularly once the sun goes down!
That was an advert on behalf of the South Dorset Tourist Board...