It is my quick guess that it is the battery. The small voltage increase may affect the reading, although on some cameras (Pentax) the voltage doesn't seem to matter. There are several ways you can get around this, the simplest and quickest is to alter the ISO rating of your film on the camera meter to bring the needle back down to what it should be. The 2nd and possibly the most satisfactory is to get a device that reduces the voltage of a 1.5V silver oxide cell down to 1.35V.
I don't know if they are available where you are but in UK there is a company called 'The small battery Company' Just Google the name and you will get their site. This device is designed to fit the socket where the old Mercury cell fitted and a smaller silver oxide cell fits inside. This has electronics that reduce the voltage from 1.5v to 1.35v.
The downside is they are a little pricey. In UK pounds they are about £20 so multiply that by 1.5 and add shipping, you are looking at around $30 each The upside is the silver cells are a lot cheaper than zinc/air type and last longer too.