One-hot encoding with values other than 1
If you use 0s and 1s, the design matrix is composed of indicators variable. An indicator variable tells the presence (1) or absence (0) of a variable. The model weights are the magnitude. If you choose something other than boolean values, the model weight will the relative weights to the larger values in the design matrix.
Additionally if you also have numeric values and are fitting a linear model, you should standardize the numeric values. Then all variables are scale from 0 to 1 which allows the model to learn better and faster.