Drop JPGs. Each is written as PNG, which keeps every decoded pixel exactly. The byte count of the PNG is shown next to the JPG's, so the size cost is never a surprise.
What PNG does and does not do
PNG keeps every pixel exactly. It cannot bring back detail the JPEG already discarded, and it will usually be larger — often three to ten times larger for a photograph — because it stores the JPEG's own artefacts faithfully as well.
That is still the right choice when the picture will be edited and saved again, since every further JPEG save loses a little more and a PNG loses nothing. For a photo that is only being sent or posted, the original JPG is usually the better file.
Transparency
A JPG has no transparency, so the PNG has none either. Turning a background transparent is editing rather than conversion, and this site does not do it.