The social convention that Goldsmith is exploring is the way in which women were treated in his time. Although this play is a comedy, and it is clear that Marlow's exaggerated shyness and reticence when faced with women of his own social standing and then his outgoing, lustful advances when he believes he is with a serving woman are deeply funny, at the same time they do point out a social convention that is far more serious than the humour in this play would suggest. Women of social standing were viewed not as individuals in their own right but only in terms of what they could bring to a marriage. This helps the audience understand by Mrs Hardcastle is so set on the idea of her son marrying Constance in order to secure her colonial jewels.
However, the opposite is also true, in that serving women, without any wealth or property, were often subjected to harassment from predatory males such as Marlow is presented as being when he first meets Kate in her guise as serving woman. Note how Marlow very quickly tries to make a sexual advance on Kate in this scene:
By coming close to some women they look younger still; but when we come very close indeed-- [Attempting to kiss her]
The shyness of Marlow with women of his own social standing and the contrast with his behaviour to serving women thus highlights the way in which society and in particular male society viewed women at the time of the play. They were either viewed as nothing more than a financial transaction in the first place or easy pickings in the second place, both of which demean the position of women. Arguably, Goldsmith presents Marlow's character in this way precisely to highlight the treatment of women in his society.