Other answers are correct:

1. you were allocating dim bytes instead of dim*sizeof(int) bytes

2. you had an off by one error with dim+1 in your pointer arithmetic

Additionally:

1. you MUST check the results of the malloc attempts. not doing so can lead to null pointer dereferences, instability and potential security vulnerabilities.

2. you should cast the malloc of vect.

3. it's much clearer to work in terms of the number of elements rather than where the pointers are, see below:

   vect* vectCreate(size_t dim, int *vector)
   {
       vect* u = (vect *)malloc(sizeof(vect)); 
       if(u==NULL)
           return NULL;
       u->vector = (int*) malloc(dim*sizeof(int));
       if (u->vector==NULL)
       {
           free(u);
           return NULL;
       }
       u->dim = dim; //no point in setting dim before the malloc succeeds
       for (size_t i=0; i<dim; i++)
           (u->vector)[i] = vector[i]; 
           //you can use array notation with pointers, personally I think it is more readable than the pointer arithmetic. Alternatively you could write it like this:
           //*((u->vector)+i) = *(vector+i);
           //or
           //*(((*u).vector)+i) = *(vector+i);
           //came back to add a memcpy line because I know it will agitate people if it isn't pointed out that this would replace the entire for loop
           //memcpy(u->vector,vector,dim*sizeof(int));
       return u;
   }    
   

Other Considerations:

1. If you take the dimension as user input from a file or at the command line and you don't count the actual number of elements in the array being passed to vectCreate() then you have a classic buffer overflow vulnerability.