Most routers have a function to open and forward ports. But it doesn't have to be same port to same port. You can open an external port and forward it to a different internal port. For example you can externally open port 8080 but forward it internally to 80. That is how you get around port 80 being blocked by most ISP companies.
If your router doesn't support this feature then replace your router. If you are using what the ISP gave you then you should replace it anyway for many other reasons. I recommend the Asus RT-AC68U. It supports mesh with more than one of these. Or if you need more coverage and don't want to deal with mesh the get the RT-AC5300, which also can become mesh if you later want. These are wireless or wired mesh (your choice).
BUT... before you open a port you should ensure that the port you are opening is secured. Does Acuparse provide a login? Is it encrypted authentication? Because if not then you are exposing the system to the outside world. You may think ah who cares. But a compromised system can be used for many things not just spying on you and looking at your weather. It can become part of a botnet and rob you of bandwidth. And then you are helping to spread evil.
A solution instead of opening up a firewall port to an insecured device is to make your router a VPN endpoint. The routers I recommended support OpenVPN which have available a free client that you can install on your computer or mobile that will be connecting to your router's VPN remotely. Once you establish a VPN connection to your home router you will have access to all internal devices as if you were home. So you'll be able to access port 80 on that internal IP address directly from anywhere. OpenVPN is free.
A simpler solution to the VPN, is to create a remote access connection to a computer. Then you remotely control that system to then talk to whatever other internal device. Perhaps you can even create a direct remote access to the very computer that is running Acuparse. There are many remote system access solutions. But this is not as elegant of an experience from a mobile device. By remote access I'm referring to Microsoft's Remote Desktop Client access that is built into Windows 10 Pro as the host (but you can use Windows Home as a client or a mobile device app), or you can use a remote access software like TeamViewer or LogMeIn or GoToMyPC or many others.