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I've a 19 hour overnight layover in Dublin (arriving in Dublin at 8 40 pm, flying out at 1 30 pm next day). As far as I can correctly identify the flight carriers, the first leg of the journey (from UK to Dublin) is by Aer Lingus and the next leg (from Dublin to France) is by Stobart Air. Both the flights have been booked together though.

How likely is that my baggage will be checked through to the final destination? If not, is there any option for me to have my baggage checked till Dublin and then to re-check it in Dublin the next day, even if I already have both the boarding passes?

The Aer Lingus website mentions:

We’ll happily through-check you and your baggage onto any airline with a baggage agreement in place. This can only happen if you’ve documentation of the itinerary showing Aer Lingus and the partner carrier flights on the same ticket.

Which to me is expressed almost as a concession – that through-checking is not your right. Very indirect but some indication that they do not require luggage to be through-checked.

Undoubtedly some airlines can be touchy about such, for fear you are going to "jump ship" in Dublin as part of a hidden city ticketing scam. However given its location I think negligible chance of that at DUB therefore a request to check bags only as far as Dublin should raise no eyebrows. In any case a 19 hour layover is a very good excuse for reclaiming bags on route - airlines don't expect one to go without a change of clothes or proper ablutions for a whole day up to a layover and goodness knows how long after.

The amount of handling should not differ, whether on and off a conveyor or in and out of a storage area so should not have any cost impact on the airline. What's left is essentially reduced risk of having to offload your bag from the Paris plane should you fail to turn up for your connection for some reason.

This is trying to apply some logic to the implications of various options, to help assess what may and what may not be allowed (despite that logic may play very little part!) but though I cannot find support for this I do know that it was perfectly normal to allow luggage to be collected at a layover location and then rechecked later even when a 'single' fight (eg an overnight stop during London to Bombay, with accommodation provided in the airline's own hotel).

Nowadays the issue is rather the opposite, inability to interline baggage across tickets causing serious transit visa problems.

The only real concern is to remember specifically to ask at the check-in counter for your flight to Dublin that you luggage NOT be checked through. Stobart Air codeshares with Aer Lingus and operates Aer Lingus Regional so it might otherwise automatically be checked-through.