Let's make sure we understand what you are starting with:

In [7]: weights
Out[7]: 
[array([[-2.66665269,  0.        ],
        [-0.36358187,  0.        ],
        [ 1.55058871,  0.        ],
        [ 3.91364328,  0.        ]]), array([[ 0.],
        [ 0.]])]
In [8]: len(weights)
Out[8]: 2
In [9]: weights[0]
Out[9]: 
array([[-2.66665269,  0.        ],
       [-0.36358187,  0.        ],
       [ 1.55058871,  0.        ],
       [ 3.91364328,  0.        ]])
In [10]: weights[0].dtype
Out[10]: dtype('float64')
In [11]: weights[0].shape
Out[11]: (4, 2)

In [13]: weights[1]
Out[13]: 
array([[ 0.],
       [ 0.]])
In [14]: weights[1].dtype
Out[14]: dtype('float64')
In [15]: weights[1].shape
Out[15]: (2, 1)

This is a 2 item list, containing two arrays. Both are 2d float.

First you wrap the whole list in an object array:

In [16]: duh =np.array(weights,dtype='object')
In [17]: duh
Out[17]: 
array([ array([[-2.66665269,  0.        ],
       [-0.36358187,  0.        ],
       [ 1.55058871,  0.        ],
       [ 3.91364328,  0.        ]]),
       array([[ 0.],
       [ 0.]])], dtype=object)

This is a 2 element array, shape (2,). But it doesn't change the nature of the elements. And there's a potential gotcha - if the element arrays had the same shape, it would have created a 3d array of objects.

This is not the right syntax for change the dtype of an array. dtype is not a writable property/attribute.

weights[1].dtype='object'

We can use astype instead:

In [19]: weights[1].astype(object)
Out[19]: 
array([[0.0],
       [0.0]], dtype=object)
In [20]: weights[1]=weights[1].astype(object)
In [21]: weights
Out[21]: 
[array([[-2.66665269,  0.        ],
        [-0.36358187,  0.        ],
        [ 1.55058871,  0.        ],
        [ 3.91364328,  0.        ]]), array([[0.0],
        [0.0]], dtype=object)]

It makes a new array, which we'd have write back into the original list.

Now I can change an element of that 2nd array

In [22]: weights[1][0,0]=None
In [23]: weights
Out[23]: 
[array([[-2.66665269,  0.        ],
        [-0.36358187,  0.        ],
        [ 1.55058871,  0.        ],
        [ 3.91364328,  0.        ]]), array([[None],
        [0.0]], dtype=object)]

When playing games like this you have to pay attention to where you have arrays and where they are lists. And pay attention to the shape and dtype of the arrays. Don't blindly index and hope for the best. Display/print these attributes, or the whole array if it isn't too large.

The solution is that numpy requires a single tuple or list of tuples. Not a list of lists or list.

The following works

 np.array((1, 1.0), dtype={'names': names, 'formats': formats})

I find it frustrating that numpy gives no indication in the error that this is what is expected.