This is the 9645th most frequent German word.
mättle
"mättle" is a dialectal term in Alemannic German meaning "to eat in moderation" or "to have a small meal."
Here 'müde' relates to 'mättle' as a dialect word meaning 'tired'.
Beim Wandern machte uns die starke Sonne sehr müde, sodass wir uns setzen mussten, um uns zu erholen.
When hiking, the strong sun made us very tired, so we had to sit down to recover.
This shows a direct association of 'mättle' with states of exhaustion or fatigue.
Nach dem anstrengenden Tag fühlte sich die Schülerin völlig matt und wollte nur noch schlafen.
After the exhausting day, the student felt completely weary and just wanted to sleep.
The use of 'mättle' here indicates physical tiredness post labor.