Hi Dianne!

Hopefully, the tissue-paper look is way late in the game of life! But before that stage, there are a few things you can do. True, mature skin quality is not the same as a young woman, but body care treaments can make a big difference, along with an effective body butter(like shea butter, or extra-virgin coconut oil, more about that in a minute!). It can be as simple as a weekly home-made olive oil-brown sugar scrub followed by the body butter, or you can go the commercial route with scrubs, creams(stay away from the cheap mineral oil-based lotions-they do nothing but sit on the skin, and the mineral oil actually DRIES out the skin in due time, making you have to apply more and more lotion for lessening benefit, if any). There are lots of "spa-type" of products out there, in differing price ranges, so this might be the time to treat oneself to a good duo! This will lessen the appearance of crepey skin, and the self-care will make you feel good too. Maybe hubby/significant other can help! Too many times, women only take care of the skin on the face, and never apply anything to the body, esp. when they get older, thinking it won't make any difference. You can delay crepey skin by not regularly getting too tan, too, as too much sun is well-known for breaking down the collagen and negatively affecting skin texture. Compare the skin on the inside of the thigh, say, to your forearm, and you'll see what I mean.
More about extra-virgin coconut oil - some women swear that within about 6 weeks of daily use on the body, crepey skin was GREATLY lessened. This type of coconut oil has a natural exfoliating acid in it, lauric acid, that smooths the skin, plus it is non-toxic to boot. Google "extra-virgin coconut oil. For my own use, I make my shea butter-coconut oil body butter, and in my next batch I'm switching from regular coconut oil to the extra-virgin kind. Another thing to consider for general health, esp. with applying something to your whole body, 60% of what you put on your skin gets absorbed into the bloodstream, not good when contemplating the amount of chemicals etc. in commercial treatments. That's why I go the natural route, personally.
About the fats, well, yes, you might have to take another look at your diet, and the type of fats you are eating. Too many refined carbos might also be the culprit here, as any excess carbohydrate esp. in refined form, tends to get stored as bodyfat. Finally, it might also boil down to your basic starting bodytype too, whether ectomorphic(basically lean), mesomorphic(puts on muscle easily), or endomorphic(puts on fat easily, tough to lose weight). Most of us have a predominant one, with a close second. Training and diet can be adjusted accordingly.
Hope this helps!