We can change the definition of things whenever it is useful. Definitions serve us. If a definition isn't useful, individuals and communities change it, sometimes on the fly, sometimes in context, sometimes explicitly, sometimes implicitly.
In everyday experience, weight is a scalar. You don't write down the direction of the weight of the bananas you buy. Insisting it is a vector is not useful in this context, and definitions exist to both clarify communication and solve problems.
Does adding the direction to the weight of the banana help solve any problems? Or is it noise? Is the scalar weight of the banana a communication problem in this case?
There are going to be other contexts where you will want weight to be a vector; maybe when calculating orbital mechanics of your banana. Even there, weight may not be a useful concept, because there are much better ways to solve orbital mechanics than talking about the directional weight of things (field potentials, say).
In formal mathematics, very specific and exact definitions are used to permit abstractions that don't match any physical situation to be discussed and delt with in a uniform way. Formal mathematics is often pillaged by physics, but physics isn't formal mathematics.
Physicists and Engineers will go off and talk about dirac delta functions whose value is 0 everywhere except at 0, and whose integral from any negative value to a positive one is 1, and then they convolve it with another function.
Now, there are ways to formalize this, but for the most part Physicists and Engineers don't bother. "The Dirac Delta isn't a function" is useful when formalizing it, but isn't nearly as useful when working with it. Knowing the formalization can be useful to avoid possible pitfalls, but it isn't usually useful when trying to use it as a tool to predict behaviour of some system.
Physics is a game of using mathematics (or whatever other tool is handy) to predict (and sometimes explain) the behavior of physical systems. There are often multiple different mathematical games, and you will use different ones for different systems. Newtonian dynamics is a game that works within its domain, and in it velocity is additive. Relativity is a game that is overly complex for some domains, but covers some territory that Newtonian dynamics doesn't cover; in Relativity, velocity isn't additive. Within Newtonian dynamics, velocity is a simple vector in a Euclidean space. Within Relativity, it isn't a simple vector in a Euclidean space.
Weight is a scalar within some games of Physics. In others, it may not be. In almost every reasonable situation you will experience, Weight will be a Scalar, because in almost every game of Physics where the direction of Weight is important, using a vector-based Weight isn't going to be the best tool you have.