The route looped round the NE of the "island" (strictly, a tombolo) and ascended the East coast before turning inland to continue climbing through a deep cutting to Easton Station. This is in the centre of Portland, and the railway did continue for perhaps half a mile further Northwards to coal and stone yards, but really only as a long siding,
There were one or two branches to the masonry works, as well.
There are traces of the old horse-drawn quarry tramways in many parts of Portland. Some run round the West slopes of The Verne, giving an attractive footpath with fine views; while a point on the Old Verne Road gives a rather impressive view along a cutting bridged by arched stone bridges.
Their rails were held down by spikes set in lead, in holes cut in the tops of stone blocks set in the ground and still extensively visible.
These tramways though, pre-date but not predecess the line from Weymouth. That railway was built completely from new, and prior to that, stone was taken away by ship. There was no continuous road either to the mainland until the late-19C, when a bridge finally replaced the passenger ferry across the Fleet's hazardous Smallmouth entrance.
The Portland Branch Line had another important stopping-place, the Whiteheads Torpedo Factory at Wyke Regis, and adjacent to the road and rail bridges across Smallmouth. The factory was served by a private siding, and also had a two-foot gauge railway of its own that ran beneath the "main" line and out along the Torpedo Testing Pier. This has gone but its footings are often clearly visible in the shallow water, as two parallel lines of square blocks. The factory itself has gone too, after some years under new ownership making engine cylinder liners, and the site is now a small housing-estate with a commemorative plinth in its centre.
From the edge of Weymouth to Smallmouth the formation has been asphalted to create a popular walking / cycling route called The Rodwell Trail. (Rodwell is the well-to-do Victorian suburb the line once served rather over-expensively with a two-road station and signal-box!) Why "Trail", I have no idea… To sound American?
The formation is still ballast across the causeway as far its disappearance under the roads and buildings of a trading-estate on the former Royal Naval Air Station and fuel-oil depot. A large, open grassed area between this and the Victoria Square "entrance" to Portland is part of the Portland Station site. Further round, in Castletown, the railway's former route past what was the Naval Base (served by private sidings) is sealed from the public, within what is now the commercial Portland Port.
You can regain it on foot below The Grove, entailing travelling to "Tophill" and following a steep footpath down the cliff, then follow it Southwards to join paths serving Church Ope Cove and a cliff-top path from The Grove. The cutting started here but has been obliterated by quarrying.
Close to Church Ope is Portland Museum, worth a visit for its displays on the local geology, stone trade, RN involvement etc. The Museum building was originally two cottages bought in run-down state and refurbished, for using as Portland Museum, by Dr. Marie Stopes, the palaeobotanist and women's health campaigner, who lived elsewhere on the "Isle".
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I have never read any of Hardy's novels, despite being a near-native of Dorset (I suppose moving here when 7 might just excuse my being an offcumden.) I have heard many say his works are bleak, but let's face it, he was writing about a very bleak world very far removed from the second-homes' vistas. Rural it was, bucolic no, romantic not at all.