The information provided here is not a replacement for a doctor. You shouldn't use it for the purpose of self-diagnosing or self-medicating but rather so you can have a more informed discussion with a professional TCM practitioner.
In Chinese Medicine weak pulse can be treated by two herbs that we have on record. Here is the list below.
Because it is a herb specifically indicated to treat weak pulse as can be seen on Ginseng's page.
Its main actions are: Very strongly tonifies the Qi. Tonifies the Lungs and Spleen. Assists the body in the secretion of Fluids and stops thirst. Strengthens the Heart and calms the Shen (mind/spirit).
Because it is a herb specifically indicated to treat weak pulse as can be seen on Prepared Aconite's page.
Its main actions are: Raises the collapse of Yang. Warms the meridians and relieves pain caused by Cold. Reduces Damp caused by Deficiency in Yang.