Normal walking speed is not reduced for a player over the limit, so toggling the movement rate from run to walk has no noticeable effect. However, if the Lone Wanderer or the Courier is over the weight limit ( Over-encumbered), their movement is limited to walking speed and the player is unable to jump. The Vault Dweller, the Chosen One, the Warrior and their companions, will be completely unable to carry more than their carry weight, making inventory management quite important in the later part of the game. Strength can affect the weight that can be carried.
Being exactly at the weight limit will not affect player movement the player is only penalized for going over the limit. The weight limit is a threshold that if surpassed, limits player movement until the weight carried matches or drops below the threshold. The weight limit is not a hard-limit that prevents you from carrying more items. The weight values show up as a fraction to the right of the Wg label, with the total amount of weight carried coming first, and the weight limit coming after the /.
The amount of weight the player is carrying and the total weight limit ( carry weight) is shown in the Pip-Boy along the top of the display while the items button is selected.