I'm on a limited-data mobile phone plan. Is there an option to only upload images when connected to Wi-Fi?

There isn't currently an option to prevent image uploads over mobile service. The easiest way to prevent using mobile data is to set the phone to airplane mode and perform the capture. When you are back to a Wi-Fi network, turn airplane mode off and launch the HeavyWorth app and it will upload the images and sync the data. If you wish to retain notifications and the ability to make and receive phone calls while using the app without it using mobile data, there are third-party firewall apps that you can use to prevent specific apps from using mobile data.