Premiere Cut Video but Export File Size Bloats I have a TV commercial that was sent to me that weighs in at 2.4mb .mp4 (MPEG Movie)

The people who made the commercial have a 5second credit title on the front of the commercial that I need to remove.

When I crop that out in Adobe Premier then export it, no matter what I do cannot get the file size anywhere near 2.4mb

I have tried Export "Match sequence settings", I have tried H.264, medium and high bit rates but all of these make the file blow out to 8 to 14mb.

Is there something I am missing here or need to be doing? Or is this just how Premier is?

I have never used Final Cut Pro and see that it has a $500 price tag but are thinking about giving it a go.

Any help would be great.
Match sequence settings confuses a lot of people. It doesn't mean the output will match the bitrate of your source files—after all you could use any number of source files in a sequence with all sorts of bitrates. Match sequence means the output will have the same frame size, fps, PAR and so on as the sequence.

Basically, if you want to get your output below a certain size you have to wind down the video bitrate, reducing the quality until it produces the desired result (you can use a bit of maths to get in the ballpark: calculate (the desired size in Mbits) / (length in seconds) and you'll have the Mbits per second budget you need to work towards.