Video files are larger after conversion
MKV and MP4 are container formats. AVC is encoding format. File size does not depend much on container type, although some containers allow for smaller file sizes, like MKV takes less space than TS because metadata is not repeated in the stream.

The single defining parameter of file size is data rate. Depending on the encoding format, frame size and frame rate you should select a reasonable data rate when encoding. Say, 5 Mbit/s for MPEG-2 Part 2 may be too low for HD video, but more than enough if you choose AVC/H.264.

Also, "mb" means "millibits". If you wanted to write "megabytes" you should have capitalized both "m" and "b".