Quality and size are a trade-off
JPEG compression works by discarding detail your eye is unlikely to notice. At 90% quality the file is large and virtually identical to the original. At 50% it is dramatically smaller, with slight softening in fine detail. Somewhere between 60% and 75% is usually the sweet spot.
Compress or resize?
These are different things. Compressing keeps the same dimensions but stores them more efficiently. Resizing reduces the actual pixel dimensions. For a website banner, resizing first and then compressing gives by far the smallest file.
When the result gets bigger
If you set quality very high on a photo that was already compressed, the output can end up larger than the original. That is normal — simply lower the quality slider and try again.