Dressing up makes it more fun
I'm a fan and a regular at the Met Saturday matinée. The performance you are going to on April 6 is on a Friday evening, and if I were going to be in a seat at that performance anywhere but the Family Circle - which tends to be more casual - I would certainly wear something chic and dressy, not "business casual". Dinner at the Met Grand Tier restaurant is indeed a great experience and definitely formal (and pretty pricey, too). I disagree that it is impossible to be overdressed - anyone in formal attire (black tie, cocktail dress) at the Saturday matinee would be overdressed, and ball gowns are strictly for the opening night gala and other galas (always identified as such on the very helpful website). I just think that dressing up is part of the fun, and even in a standing place at the matinée (shh ... best bargain in New York) I'd avoid jeans and sneakers. Opera is not stuffy nor is it only for what some politicians refer to as the "cultural élite" but it IS special and magical, and I find that dressing up a little helps me enjoy the magnificent music, brilliant performances, world-class orchestra and awesome auditorium even more. I'm sure you will have a lovely time, I hope you do!