Is a corpulent person who feels ashamed to go to the mosque for congregational prayers (except for Fajr and Isha, when the number of worshippers is smaller) excused for not attending congregational prayers at the mosque?

Congregational prayer is obligatory for able-bodied men, whether at home or traveling. Feeling embarrassed is not an excuse to abandon this obligation. You should not pay attention to what people think, and you should strengthen your resolve and make prayer a motivation for you to leave your home. However, if there is clear hardship in walking to the prayer, this is an excuse that permits abstaining from the congregation. An excuse for abandoning Friday prayer and congregational prayer is being ill or fearing the onset or worsening of an illness, because when the Prophet, peace and blessings be upon him, fell ill, he stayed away from the mosque.