Going from bi weekly to weekly shouldn't make a different or cause you to get 2 W2 forms. Betrter check with your employer.
If the EIN is the same and you work in more than 1 state or city, sometimes they will give you another W2 with the extra state information on it and the top part the same or not filled in. If this is the case, enter 1 W-2 but include both state and local taxes on it. It will let you type in more than one line for boxes 15-20. Don’t add the boxes together. If the locality in box 20 is the same you can simply combine the values in boxes 18 and then the values in box 19 together.
Same for boxes 12 and 14 if there is no room on the first W2 they can give you another W2 with the extra boxes on it. So list them all on 1 W2. For box 12 just enter it in the next row or box. It doesn’t have to match the box 12 a-d etc.