Check on the website of your state's department of transportation for information on livestock load restrictions for the state, as these restrictions often apply also to local communities. Also check enactments of your state legislature on vehicle loads, some of which also cover livestock loads.
For example, the website of the Missouri Department of Transportation posts information about vehicle loads. As of 2016, a recent example is the state's 2015 legislation increasing the weight amounts for livestock and grain transportation. The website provides two documents, the Maximum Allowable Weight for Grain and Grain Co-Products and Legal Weight Limits on Missouri Highways, that detail the exact amounts. The documents are in PDF format, and the Maximum Allowable Weight for Grain and Grain Co-Products document list weight types in correspondence with the number of axles on a transporting vehicle that is traveling on a highway within the state.
The Michigan Legislature website offers legislation on livestock and other vehicle loads from different years in the state's history. It sometimes refers to livestock alongside other farm items under the name "agricultural commodities." Some documents, such as § 20-116 from the North Carolina Legislature, produce general vehicle weight guidelines that specifically exempt livestock transporters.