This type of stock character probably stems from a conglomeration of many historical "types," but for my answer, I'm going to stick to Western European traditions as that is the contemporary frame for the character you're describing.
This question requires first that we understand what a stock character is, exactly. Because we're working within a European theatre historical frame here, we can look to Roman drama for some information. Specifically, Timothy J. Moore, in his book Roman Theatre (55), describes the cultural popularity and growth of stock characters in the comedic plays of Terence and Plautus. Indeed, these plays often include a character commonly named Simo (see Terence's play Andria) who is an older man, usually a father to one of the romantic leads, that is pretty easy-going and dismissive of their child's indiscretions and antics - as long as it doesn't affect Simo directly (particularly in his social standing). Roman comedies, especially those by Terence, were definitely known, read, and copied in the European Middle Ages and a tradition of folk performances derived from these plays may have contributed to the development of Commedia dell'Arte in Italy during the central and late medieval period. Commedia relies on stock characters as a type of folk-theatre from which the audience can quickly identify a "type" of person (often a lampooned stereotype of from a different region of the Italian peninsula) in order to place them within pre-formatted plot arcs from which the situational humor is quickly palpable. So, I'm going to focus on two European stock characters that developed after the Middle Ages and through the early modern period: the Italian Il Dottore and the German Hanswurst.
Commedia gives us the Il Dottore character: an older parent to one of the young lovers (innamorati) that, though he is educated, is rude, gluttonous, potentially a drunkard, and certainly leans an ear to crass and uncouth subject matter. He often attempts to set up his son or daughter with the child of his commedia counterpart: Pantalone. But because Pantalone is more concerned with his social status and a "proper" marriage for his son/daughter, he usually looks down upon Il Dottore as an upstart and socially unrefined. Their interactions create a great deal of humor.
The Hanswurst character does not come directly from commedia, but the Il Dottore character may have influenced his appearance and/or development in German comedy beginning in the 16th century (commedia is older). Like Il Dottore, Hanswurst is a stock character created from German folk theatre that was highly popular across all social classes - though he shows up in some "high comedy" as well. He's considered to be the creation of Sebastian Brant from the late-15th-century play, Daß Narrenschyff ad Narragoniam. He is very much a buffoon who is self-indulgent to the point of extravagant gluttony. This makes him a "punching-bag" character made fun of and beaten up by other characters in the play. Nevertheless, he keeps a happy demeanor (probably because he drank too much beer) and required strong physical and acrobatic abilities from the actor playing him - after all, he falls down a lot. Martin Luther even uses Hanswurst to analogize and criticize the excesses of the Catholic Church in the 16th century. He's probably the closest thing to a Homer Simpson you'll find in theatre history.
Just for FYI: I'm a PhD candidate in Theatre specializing in European Theatre history. DM if you'd like a bibliography for this. Enjoyed the question!
EDIT: Here are the sources I've used and you should check out too:
This type of stock character probably stems from a conglomeration of many historical "types," but for my answer, I'm going to stick to Western European traditions as that is the contemporary frame for the character you're describing.
This question requires first that we understand what a stock character is, exactly. Because we're working within a European theatre historical frame here, we can look to Roman drama for some information. Specifically, Timothy J. Moore, in his book Roman Theatre (55), describes the cultural popularity and growth of stock characters in the comedic plays of Terence and Plautus. Indeed, these plays often include a character commonly named Simo (see Terence's play Andria) who is an older man, usually a father to one of the romantic leads, that is pretty easy-going and dismissive of their child's indiscretions and antics - as long as it doesn't affect Simo directly (particularly in his social standing). Roman comedies, especially those by Terence, were definitely known, read, and copied in the European Middle Ages and a tradition of folk performances derived from these plays may have contributed to the development of Commedia dell'Arte in Italy during the central and late medieval period. Commedia relies on stock characters as a type of folk-theatre from which the audience can quickly identify a "type" of person (often a lampooned stereotype of from a different region of the Italian peninsula) in order to place them within pre-formatted plot arcs from which the situational humor is quickly palpable. So, I'm going to focus on two European stock characters that developed after the Middle Ages and through the early modern period: the Italian Il Dottore and the German Hanswurst.
Commedia gives us the Il Dottore character: an older parent to one of the young lovers (innamorati) that, though he is educated, is rude, gluttonous, potentially a drunkard, and certainly leans an ear to crass and uncouth subject matter. He often attempts to set up his son or daughter with the child of his commedia counterpart: Pantalone. But because Pantalone is more concerned with his social status and a "proper" marriage for his son/daughter, he usually looks down upon Il Dottore as an upstart and socially unrefined. Their interactions create a great deal of humor.
The Hanswurst character does not come directly from commedia, but the Il Dottore character may have influenced his appearance and/or development in German comedy beginning in the 16th century (commedia is older). Like Il Dottore, Hanswurst is a stock character created from German folk theatre that was highly popular across all social classes - though he shows up in some "high comedy" as well. He's considered to be the creation of Sebastian Brant from the late-15th-century play, Daß Narrenschyff ad Narragoniam. He is very much a buffoon who is self-indulgent to the point of extravagant gluttony. This makes him a "punching-bag" character made fun of and beaten up by other characters in the play. Nevertheless, he keeps a happy demeanor (probably because he drank too much beer) and required strong physical and acrobatic abilities from the actor playing him - after all, he falls down a lot. Martin Luther even uses Hanswurst to analogize and criticize the excesses of the Catholic Church in the 16th century. He's probably the closest thing to a Homer Simpson you'll find in theatre history.
Just for FYI: I'm a PhD candidate in Theatre specializing in European Theatre history. DM if you'd like a bibliography for this. Enjoyed the question!
EDIT: Here are the sources I've used and you should check out too: