WeatherCat is sending the message as an email, the cellular provider is taking the email and delivering it as an SMS message.
You need to configure the SMTP server section in WeatherCat Preferences to send messages using an email account, attached below is a sample of how to set it up.
I have a web host account for my weather station, so I am using an email account setup just for WeatherCat to send messages to my email account and text to my phone.
If you have an email account setup with an Internet service provider, then you could use that account for sending emails in WeatherCat. You could try sending using port 25 without a user and password, but most service providers block port 25 and require authentication to prevent spamming.