To take advantage of the best prices you will need to prove you are a leisure traveller, on the way to the airport, so you will need to provide either yr flight numbers or yr holiday booking reference. I don't think you will need to provide this when you arrive at the station but you may be asked to give them on your travels from the station to the airport.
Going to the airport on the train is great, you can sleep, read a book (even at night), play travel scrabble, or just stare out of the window... The other caveat to buying these cheap train tickets from the station to gatwick airport is that there must be at least two grown ups travelling together. But another great advantage is that kids go free. All children under 5 go free, and then one child over five but under 16 per adult travelling on the train to the airport.
be sure to leave plenty of time to get to the airport early enough to eat, shop and so on, so check the times of trains from weymouth station before you go. If you end up with time to kill at gatwick airport you can always read a book or play travel scrabble again! As you have bought your train ticket in advance, you don't need to worry about the opening hours of weymouth station.
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