This tutorial can be useful: http://www.exoguru.com/android/material-design/navigation/android-sliding-tabs-with-material-design.html

Use a bar chart(?) on the home screen that displays the progress over time.

This chart should be per session.

Progress could be:

• average grade of the session (in which case we need to convert grades to numbers and compute a decimal number)
• maximum grade of the session

A long list of grades is ok for a watch, but not suited for phones.

Maybe use a 2d picker like this:

...
5- 5 5+
6- 6 6+
7- 7 7+
...

This would probably require to define a new kind of climbing data type for Google Fit.

https://developers.google.com/fit/android/data-types (see Android samples)

Today the wearable can only enter climbs.
It could be nice to display the grades of the X latest climbs. Maybe at the top of the picker?

Today the list is justified to the left, which does not work great on round watched.

It's probably best to center the items as a first step.

Today the position is recorded from the phone, which can be different from the wearable position if the climber is not next to his phone.

See https://developer.android.com/training/articles/wear-location-detection.html