I do, but not the rest of my family - really. To some extent they do but not as full as I do. I started not eating any grains at all after being advised to be gluten free, and since all grains have inflammatory lectins etc I decided to cut them all out. I do use buckwheat (which is a seed anyway). I eat meats, fish, eggs, nuts, seeds, veggies and fruit. Some paleo types eat dairy, some don’t - most don’t since agriculture is modern human ‘invention’ and paleo’s strive to eat pre-agricultural era. This is based, I think, on the premise that the human body takes about 70-100 thousand years to show even slight adaptation to something (say a slight increase in sugar or grain in the diet) and we have only been living and eating as an agricultural based society for about 4000 yrs, max. There is a lot of interesting theory and research on this. I would suggest the interesting book Primal Body Primal Mind as a starting point by Nora Ged….? Um, I forget her last name! Bare in mind since the book was written the author now is dairy free, so perhaps later editions will include more on this. It is not a ‘paleo’ book, as such, it is someone who has researched nutrition and uses the evolution of human physiology (plus modern testing etc to measure results and the scouring of every bit of nutritional research) to find the ‘primal’ diet of humans. It closely resembles the paleo style of eating.
I was weighing in at 10 and a half stone after my dd was born and after a year eating this way I weighed 8 and a half. I am pregnant now again and have strongly wanted sme dairy and rice so I have been eating them. I am flexible and never did it anyway for the weight, I was wanting to decrease some inflammatory symptoms I was having and I did, plus including various supplements (like vit d - ) it worked too. It was interesting to see the weight loss as a side effect. It was suggested to me at the time that I ought to take methotrexate (a chemo drug) for two years. I totally declined. I changed my diet instead and have been in the best health of my whole adult life, with no further illness. My consultant thinks it is coincidence though, as he does not believe diet effects health 
Despite my blood work showing differently
If I eat junk, like crisps or chocolate, of even just jam, sometimes dairy - I feel very foggy headed and tired for a couple of days, and often get headaches.
Will be interested to hear other comments.
