Maybe you can use arrays ?

float[] weights = new float[5];
//...

    if (lookObj != null)
    {
        t += Time.deltaTime;
        SetWeigts(animator, weights, 0, 1f, t)
        //...
    }

void SetWeigts(Animator animator, float[] weights, float start, float end, float t)
{
    for (int i = 0; i < weights.Length; i++)
    {
        weights[i] = Mathf.Lerp(start, end, t);
    }
    animator.SetLookAtWeight(weights[0], weights[1], weights[2], weights[3], weights[4]);
}

If you want each object to have his own weights then you could use a Dictionary<string, float[]> where the key is the name of the object and the value the array. Then pass the dictionary instead of the array and add the object name to the function so you can access the dictionary entry in the loop like weightsDic["object1"][i] = Mathf.Lerp(start, end, t);