A few weeks ago my husband started snoring all the time. Is there anything we can do about it?

Recent snoring. If your husband has never snored or snored "lightly" and is now constantly snoring or it has suddenly gotten worse... I would get this checked asap. Sudden onset or recent snoring is not normal. Snoring usually progresses over time. The one exception would be an increase in snoring with allergies/cold/ or sinus infection. If there are otherwise no nasal symptoms... Get this checked by a lcoal ent.
Yes. It's possible that he has nasal congestion at night forcing him to be a mouth breather when he sleeps. This can lead to snoring. The nasal congestion can be due to allergies or a recent cold. Have your husband try otc decongestant nasal sprays and/or breathe right strips for several nights. If this doesn't work or he has pauses in his breathing, you should see an ent.
There may be. If he has recently gained some weight it can explain it. A 10% loss of body weight can reduce snoring by over 50%. If he had a cold recently it may have turned into a mild sinus infection which can block up his nose leading to mouth breathing that can cause or worsen snoring. He can try breathe right strips at night. An ENT physician should be able to examine his airway and give you a good answer.