Ibn 'Umar said that the Messenger of Allah ﷺ used to deliver the sermon on Friday while standing. He would then sit and then stand (for the second sermon) as they (the Muslims) do nowadays.  

كَانَ رَسُولُ اللَّهِ ﷺ يَخْطُبُ يَوْمَ الْجُمُعَةِ قَائِمًا ثُمَّ يَجْلِسُ ثُمَّ يَقُومُ قَالَ كَمَا يَفْعَلُونَ الْيَوْمَ  

The Apostle of Allah ﷺ gave two sermons between which he sat, recited the Qur'an and exhorted the people.  

كَانَتْ لِلنَّبِيِّ ﷺ خُطْبَتَانِ يَجْلِسُ بَيْنَهُمَا يَقْرَأُ الْقُرْآنَ وَيُذَكِّرُ النَّاسَ  

Jabir b. Samura said that the Messenger of Allah ﷺ used to deliver the sermon while standing. He would then sit down and then stand up and address in a standing posture; and whoever informed you that he (the Holy Prophet) delivered the sermon while sitting told a lie. By Allah. I prayed with him more than two thousand times.  

أَنَّ رَسُولَ اللَّهِ ﷺ كَانَ يَخْطُبُ قَائِمًا ثُمَّ يَجْلِسُ ثُمَّ يَقُومُ فَيَخْطُبُ قَائِمًا فَمَنْ نَبَّأَكَ أَنَّهُ كَانَ يَخْطُبُ جَالِسًا فَقَدْ كَذَبَ فَقَدْ وَاللَّهِ صَلَّيْتُ مَعَهُ أَكْثَرَ مِنْ أَلْفَىْ صَلاَةٍ