You are able to take breaks but since 9/11 it’s become a bit of a hassle. Security is paramount since there are some very bad people out there that would LOVE the opportunity to enter the cockpit. Every airline has a procedure for how it’s done and that information is considered “Sensitive Secure” and not to be disclosed. Short answer, yes you can take breaks but we generally keep them to a minimum.
First EVERY plane has a maximum cruise speed (Vmo/Mmo) and as long as you don’t exceed that structure is not an issue (unless you’re in turbulence). The main factor is cost. Jet fuel ain’t cheap and the faster you fly the more you burn, the CEO and shareholders don’t like that, they yell at the Director of Flight Ops, he yells at the Chief Pilot then he yells at you! Now when I was at ExpressJet, the RJ was a very efficient jet and most of the flights were fairly short so no one got too twisted if we went ludicrous speed. Same thing at Hawaiian when I flew the 717 Interisland. The longest flight is HNL-ITO (130nm and about 32min), fly fast or slow, the fuel burn difference is negligible. BUT, now I’m on the A330, flying 3000nm+ and 5hrs + and flying fast equates to thousands of pounds of fuel and that adds up. Is that to say you can’t ever pick it up? No, but you best have a good reason.
Now you also mentioned “beating” the weather and that opens a whole other conversation. Fuel planning is a really big deal in commercial aviation. There’s always a balance (sometimes a battle) between efficiency and safety. Fuel has weight and weight increases fuel burn. The company always wants you to carry less while pilots always like more (slightly off topic but more fuel is almost always a good thing unless you have an emergency at takeoff and you’re overweight for landing and have to dump, otherwise fuel gives you options). When fuel is planned you obviously need enough to fly from A-B plus some extra based on a number of factors. Now if the forecasted weather is crappy at your destination you’ll get even more fuel to get you to an alternate airport (or 2). Cool? Ok now let’s say there’s weather coming in you’re “trying to beat” and you pick up the speed (because you’re a pilot and therefore smarter than EVERYBODY), beat the weather and land. That’s great. BUT, let’s say you’re wrong (because maybe you’re not smarter than everybody), the weather beats you, you get there but you can’t land due to the crappy weather, and you’ve cut into your alternate fuel. Best scenario you have to declare a fuel emergency, get priority handling and a call from the Chief Pilot. Worst? Well, turbine engines need fuel and heavy jets don’t really glide that well, and you end up on the 6 o’clock news.
Everyone has different goals and aspirations in aviation. Personally mine is to NEVER end up on the 6 o’clock news. That may be boring but boring with 300 passengers sitting behind you is a good thing.