Your Mac should have no I'll effect from running 24/7. Some people argue that leaving a computer on is less stressful than the daily on/off cycling.
That said using your daily use computer for weather software has some risks and compromise. You need your computer to be there for everything else you do and a system crash or a software installation will require reboots. You compromise mobility if you are tethered to a USB logger. That is why a dedicated system for running weather software addresses many risks, compromises and concerns.
A dedicated weather system need not be a typical computer that takes up space, and consumes a bunch of power. A Raspberry Pi is a small single board computer with a powerful enough processor to run an operating system and run various programs. I recommend putting a Raspberry Pi inside of a Flirc case as it will keep it cool without need of a fan. You can manage this Raspberry Pi without need for a mouse and keyboard nor monitor plugged into it. It can be managed remotely via the network using your Mac (or any other computer). Then you can turn your Mac off and the Raspberry will keep running whatever you set up. That can be Weather-Display along with many other things like a Plex server for video for your home theater or home automation software or an ad blocker for your network like Pi-hole or many other things and it can do several of these things at once (within limits as it isn't a really powerful computer, but it is decent enough to do a few things at a time). Raspberry Pi computers are so economical that many people have more than one. The Raspberry Pi has a great amount of popularity that there are tons of people available to help in various forums. There are a ton of websites with how to documentation and there are a ton of YouTube videos. It is easy to get going with it. It runs the Linux operating system with a version designed just for it called Raspberry Pi OS (previously called Raspbian). But don't let that deter you. It has a nice easy graphical display and sure you might need to copy or type some commands into the command prompt sometimes but all that will be just by following whatever guides and instructions you have for the task at hand.