Mumsnet always amazes me - the extent to which anonymous posters are so quick to hector, pressure or even shame someone into taking on a role or obligation that we have no way of knowing if they would actually be willing to do themselves. They are quite happy to pressure the OP into running a one-woman soup kitchen but, to paraphrase a famous quote: 'The problem with this approach is that you eventually run out of other people's time and money'!
Besides, as you said family of five, I imagine that you are not the only adult in the household. What is the view of your spouse or partner?
My own view is that it would be fine for her to come over one half-day each weekend. Say, 12 - 6pm, to include either lunch or supper. Plus perhaps going out together on a Friday night. Be warm and welcoming, offer her a good meal when she is with you, offer her the bus fare if she needs it and offer her a lift so that she gets home safely. But that should be it. Your duty is to your son and your other children. If you have further concerns about her wellbeing or safety then it is really school you should be speaking to - if someone effectively takes her in then this could be masking problems that outside agencies might need to know about.
Turning to your son, he is in Year 10 - I am frankly staggered as to how he finds the time to hang out with her all weekend, surely he has a ton of homework to be getting on with? Plus other uses for his time. What about:
Homework and reviewing his GCSE subject work
Reading for pleasure
Hobbies and interests
Exercise and sports
Other friendships
Volunteering - DofE etc
Careers research
Housework and cooking
He is slipping into a restricted, coupled-up lifestyle at a very young age and if you are not careful at best he will compromise his GCSE grades and overall development, or at worst, end up a very young dad.