Night time nappy leakage

I am sure there is probably a simple solution but, how do you prevent baby soaking through nappy at night? She is 17 weeks and quite the munchkin, loves her milk. She has stopped night time poos but her nappy is quite.wet that it leaks through her sleep suit at night and she ends up with a cold. I plan to change her at least halfway through, usually when she stirs, but at this point it interferes with her sleep if she is not fully awake and then I need to get up as well. I have tried sizing up and two different disposable brands with the same result. Considering giving reusable a try. Thanks for any suggestions.