Or could it be that the cutting is deep, so the deck of the bridge higher than usual?
No, because the formation is close to natural ground level.
The 1876/1897
OS▸ map on NLS shows spot heights on the road about 300' either side of the bridge, at 162' and 155'. It also shows a benchmark at the bridge of 176.4', which I would expect to be low down on the parapet (who fancies going poking about in the undergrowth for that?).
It looks as if the ground slopes pretty evenly, so let's say the natural level at the bridge is 158-159', which places the benchmark 18' (plus or minus a foot or two) above that. The typical structures gauge is a minimum of 4m above railhead, so assume the bridge was built to be above that level, say at 13-14'. To that must be added the height of the railhead above ground level (1'), an allowance for the narrow arch (1'), and the depth of the masonry up to the benchmark (say 3'). That adds up to 18-19' - so I would say the bridge is exactly the expected height.
Big things, trains.