Passer sous le nez means that you’ll miss to catch the opportunity of such a weekend.

The idea is that something of interest was very close to you but you fail or forget to catch it for some reason and now it is out of reach (gunshot even.)

I suppose the most accurate translation is “to slip through one’s fingers“.

Basically, it means you see an opportunity, you’re very close to getting it, and yet you miss.

As Stéphane highlighted, “to slip through one’s fingers” literally translates to another equivalent French “glisser entre les doigts“. It was within your grasp but when you closed your hand, it slipped away.

The context reveals a lot:

Tout le monde rêve de ce genre de week-end haut de gamme. 
(Everyone dreams of this type of upscale weekend)

Mais il vous passera sous le nez, car il est destiné... à vos chiens.
(But you will be unaware of it, because it is intended for...your dogs)

In English the expression “happen right under your nose” exists, and generally signifies something that, under normal circumstances, should catch your attention but, due to some distraction, gets ignored. Depending on the context, a direct translation may be less appropriate, so one can choose indirect synonymous expressions such as “go unnoticed”, “blind to”, “unaware of” or, even, “be oblivious to”.

It literally means “it will pass you by under your nose”.

The implication in this context is that you will see it come (close to you, right under your nose) and then see it go (away from you so that you end up not having it).

An English equivalent expression might be “so near yet so far“.

There is an English expression that gives the equivalent to « sous le nez ».
While studying the book for the answer, he missed seeing it, it was under his nose.