In my late 40s (5 years ago) I trained myself up from daily dog-walking (approx 5km per day) to walking The Ridgeway (140km) with my dog in 4 days. I did this by extending my walks to about 8km, while building up the weight I was carrying. I also wore all the kit that I would be wearing for the event itself. I did longer walks at the weekend, but nothing more than about 16km.
So after 2 months, I was ready and was carrying 19kg on my daily walks, made up of 2-litre bottles of tap water wrapped in towels to stop them squeaking.
For relative comparison, I'm 6'2", 14-15 stone (90-95kg ish), and relatively healthy. I was doing the walk for charity, which gave me an extra drive and motivation that may have pushed me a bit beyond what I should have done.
My daily splits were approximately 36km, 28km, 48km, 30km (due to a bit of bad planning regarding the 3rd day). Fortunately, I only camped out on the first night, as halfway was my home and the 3rd night it was raining so heavily that a delightful pub landlady let us sleep on the floor of the bar, rather than camp in the garden as planned.
I tried to start my days around 8am, walk till about 11, then eat and rest for 30-40 minutes. Then walk again till 2pm, a shorter rest and snack, then finish it off. On day 3 of the above it all went wrong because I overslept and mis-measured the distance, doing the last 2 hours in the dark and the last hour of that in lashing rain. Thank goodness for a border collie's nose leading the way on at least one occasion in the dark.
I ended up carrying about 15kg, which included things I didn't use, and more water than I needed. I also had food, drink and bedding for my dog too. So, I reckon that with some preparation and common sense you should be able to meet your challenge.
The Ridgeway is a pretty tame walk, and well signposted, so very little in the way of hiking knowledge was needed. It stays close to civilisation, and even passes through a few towns where water bottles can be topped up etc. So bear in mind that The Cleveland Way is a bit more challenging, and make sure you are logistically prepared with GPS, first aid etc as others have advised.
Incidentally, I did The Ridgeway again the following year in two days for a different charity. I was a wreck at the end of that, and don't recommend it to anyone!