I'm sorry you're having trouble. I'll offer what advice I can. First, I am an ex-Crossfit Trainer (Level 1, worked at two gyms) so I have some experience, and I've done every diet from Paleo, to Primal, to WAPF, to modified Paleo, etc.
First thing that might be happening is over-training. If you are beating yourself up faster than your body can recover, it will have a stress response and put on weight. This can happen when you get stronger actually, because you can handle more loads, and activate more muscle. More muscle activation requires longer recovery. Try to get lots of sleep (9 hours a night would be a good target...I know it seems impossible, but it is the ideal). If you're fatigued from lack of sleep, over-training, or both working together, you'll eat more too.
The other thing I can think of is that you're not going all out on Paleo. Even a little bit of extra sugar will mess with your insulin, and if you add to that the high fat intake of Paleo, you're in trouble. It's sort of either or. If you're okay going cold turkey, do totally Paleo or find another diet that works for you.
If you're more comfortable doing a gradual approach, back off from the aspects of Paleo like low-carb, and focus on eliminating all processed sugars (and most other sweeteners) and any refined grains. It is also really important that you get rid of ALL processed foods (my rule has always been that the ingredients label should have nothing but whole food items on it: no preservatives, no sweeteners, no 'natural flavor' no coloring). Our bodies store toxins in fat, and these chemicals stress the body out, which can also cause it to store fat. You might still be eating dairy, whole grains, legumes, etc, but focus on eliminating processed foods, sugars and white grains. Once that is taken care of (a month or two), then start thinking about doing the other parts of Paleo (higher protein, low carb, higher fat intake). Also, keep in mind that Paleo works best when its mostly vegetables. That doesn't always come across in discussions of the diet.
With all that said...stressing about food will make it a problem, no matter how healthy. I know it's not fair, and I went through that where I was eating healthier than everyone I knew, but I was always worried about what I was eating, and I was sick all the time. Once I figured out how to relax but still eat well, things improved a lot.
Sorry for the long response. I hope it's informative. I know what you're feeling and have had similar frustrations. Focus on rest and recovery from CrossFit, and check that there is zero added sugar, zero processed foods, and worry less about the other stuff until that is nailed down. Good luck.