I can tell you what having a 3 or 4 month old having teeth has to do with weaning and it's that they BITE YOU! HARD! I suffered with my son trying desperately to push through the pain of him teething at 2 months and cutting his first TWO teeth the week he turned 4 months.
They grind on your nipple with very sharp teeth where gummy babies would pull and because of the tenderness of baby gums cutting teeth...they bite down with very new sharp teeth.
Despite this excruciating pain, I tried expressing for a period so that the milk could flow easily from the bottle teat and he wouldn't have to hurt his gums pulling.
Unfortunately...any attempts soon to give him the breast were refused because it just hurt him too much to pull the milk and soon my milk supply had dropped drastically and the breastfeeding association suggested I supplement with formula to ensure he was getting enough milk and pretty soon...formula was it.
My daughter has just done exactly the same thing. She is only 18 weeks and 2 weeks ago...cut her first tooth. At present I am still breastfeeding where she'll have me, but having to supplement with formula for the times when her gums are too tender (she is cutting her second tooth) and I am simply going to move over to formula altogether because the stress is already wreaking havoc on my supply.
It was very depressing with my son. It was hard enough having people undermine me or look at me like I was a crazy person for suggesting a 2 month old baby was cutting teeth, let alone the pressure of continuing to breastfeed through such a painful time for your little baby.
Neither of my children has had any problems weaning to formula from the breast and I am very, very proud of myself for lasting as long as I did through a very stressful time. It was like going from a newborn to a teething 6month old baby in just 3 or 4 months. No break inbetween.