Hi,I'm Dr Steve. By SlatheringIam guessing that you are referring to increased salivation or slobbering. WIth that assumption, I will try to answer your question. There can be several causes of this problem including a bad tooth ( infected or broken), Infectionof the gums ( gingivitis), A sore or ulcer on the tongue or cheek to name the most common causes that I see.
Other causes could beb rabies or poisoning, but with the ccondition going on for several weeks, these las two are very unlikely. WHat needs to be done is to look in the dog's mouth and this usually requires sedation or tranquilization so that the entire mouth can be examined thoroughly. THis would be best done by a vet for two reasons. One he can give the medicine to sedate the dog so if there is a painful area in the mouth, it doesn't hurt the dog and it reduces the chance of getting bitten by looking inthe mouth. Two , once the problem is determined, proper treatment can be started and the problem can be resolved.
INcreased salivation is usually the dogs way of soothing a sore or infected area in the mouth and this is what needs to be treated with antibiotics or antiinflammatory medicines depending on the exact cause of the problem. Unfortunately with this type of a problem there isn't much that canbe done at home. I hope this has helped. If it has would you please click the submit button so I may receive credit for my answer. I will check later to see if you have more questions. Thanks for using just answer and good luck.