Pros:
1. The process of fitting a model using lwlr(locally weighted linear regression) to the sample data does not begin with the specification of a function. The analyst only has to provide a smoothing parameter value and the degree of the local polynomial.
2. It is very flexible and ideal for modeling complex processes for which no theoretical models exist.
Cons:
1. It is with high time complexity.
2. It makes less efficient use of data than other least squares methods. It requires fairly large, densely sampled data sets in order to produce good models.
3. It does not produce a regression function that is easily represented by a mathematical formula. 

University of Michigan - Ann Arbor

To make up for the under-fitting or over-fitting problems of ordinary linear regression models, locally weighted linear regression introduce weights to loss function. 
Its loss is transmitted to:
$J(\theta)=\sum_{i=1}^m w^i (y^{(i)} - \theta^T x^{(i)})^2$
w is used to represent the weights. Its value is calculated using Gaussian kernel function:
$w^i = exp(\frac{(x-x^i)^2}{-2k^2})$

Locally Weighted Linear Regression

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

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