Additionally, you might want to consider a few best practices while authoring your data in ArcGIS Pro.
1. Don't show the parcels at all scales. Choose a scale range where upto 1000 features will be shown. Set a suitable visible scale range for the Parcels layer.
Alternatively, you may also set a visible scale range in ArcGIS Online (Map Viewer).
2. Project the layer/map in Web Mercator Auxiliary Sphere (WKID 102100). This will help in faster rendering of your web layer in ArcGIS Online.
3. Publish a Hosted Feature Layer, and turn off Editing and Sync in hosted feature layer properties (Item Details Page).
4. Keep the layer symbology simple. Generalizing the features would help in decreasing the size of the shapefile/feature class, but consider its impact on the accuracy of your datasets.
5. Remove/Hide the fields that you don't want to show in the web map.
For more information, please visit the following links.
Best Practices for Map Creators
Best Practices for Layer Publishers
Think Location