The Watch Connectivity frameworks were not designed to exchange real-time information. Even Apple's health-related apps, if in the background, do not send their data to their iPhone couterpart app in real-time. If the app is in the foreground then watchOS will grant your app more resources. You should perhaps redesign to send your data in batches and/or allow the user to act on the data via a complication or a main app, if that's applicable.
Your single app tests may not be representative of an actual user's device because the user may also be using a network intensive foreground app.
If you provide details on the type of data you are sending (for example, is the data app-generated or sensor-generated), perhaps we can provide a more detailed suggestion.
--Zaid