When you hear the word "carbs" the first thing that pops into your head might be some type of grain product: bread, pasta, or pizza. In the Paleo world those foods aren't even a consideration. Sure, after all of the processing, additives, preservatives and dressing up, some of them are pretty tasty. But in terms of overall health and how you feel after you've eaten those foods, it's just not worth it.
When I'm referring to carbs, I'm talking vegetables and fruits, or starches and sugars. Cutting out the grains almost by default makes Paleo a low-carb way of eating compared to a typical American diet. But contrary to what you've heard all of your life, you don't need that many carbs in your body to get you through the day.
There's no such thing as "carb-loading" before a sporting event. Think of your glycogen storage (the sugar that's stored for energy from carbohydrates) as a gas tank on a car - you can't overfill a gas tank. Once it's topped off, that's it. The excess gas can't be stored and so it spills out all over your shoes. The same thing is happening in your body, except the excess gas is being stored as body fat and causing you to gain weight.
If leaning out or weight management is your goal, you have to look at it as earning your carbs on a day-to-day basis. If you're really active on a particular day (i.e. on your feet most of the day moving around, or doing multiple workouts at different times in the day), eat some starches (yams, sweet potato, squash, etc) and a little sugar (in the form of fruits) after that activity or activities. If you sat on your ass for the majority of the day, you can't justify those five pieces of fruit, two tablespoons of honey in your tea, three large sweet potatoes and some various Paleo dessert just because you killed some 7-minute metcon. Unfortunately, your total amount of effort doesn't justify the extra sugar. So, stick to the green leafy vegetables on your less active days and take advantage of the recovery benefits of a higher dose of starches after your workout or a long day of high activity.