The Prophet ﷺ used to deliver the sermon standing, then sit down, then stand again, just as you do now.
كان النبي ﷺ يخطب قائما، ثم يقعد، ثم يقوم، كما تفعلون الآن.
Bukhari narrated it in "Friday Prayer" (920), and Muslim in "Friday Prayer" (861), both from the hadith of Khalid bin Harith, who said, "Ubaydullah narrated to us, from Nafi, from Ibn Umar," and he mentioned it.