As NHS Behind the Headlines says:
However, these results must be interpreted in the correct context, as the risk of newborn death was very low in both groups: 4.2 out of 10,000 births in normal working hours, and 5.6 out of 10,000 births out-of-hours.
That is one third more. It is not:
'Three times more' would be 12.6 out of 10,000 - a vast difference to 5.6.
Journalist Sophie Borland gets this right in her article, but the headline writer couldn't tell the difference - either because they didn't understand it's not the same, or because 'three times more likely' sounded more sensationalist.
However, Borland doesn't get everything totally correct. Her first sentence says:
Women who give birth at night or weekends face a higher risk of their baby dying due to hospital staffing shortages, research suggests.
However, as Behind the Headlines points out:
It is misleading to report that the associations may be ‘due to hospital staffing shortages’, as the causes of different death rates have not been examined in this research and any such claims are based on speculation.
(Hat-tip to Alex P)