You need to intonate the uke. Which means you get the vibrating string length correct.
Simple and easy. All you need is an electronic tuner.
You just need to have a floating or adjustable bridge.
1-tune ( duh!)
2-play a single open string and read the note.
3-Now , fret at the octave. ( I dunno where on a uke)
---It SHOULD be at the 12th fret ( it is on a regular guitar. 8th on a dulcibox) Basically where the notes start over.
4-Read the fretted note. It should be the same as the open note.
5-If note slide the bridge back and forth until the match as close as possible.
6- Repeat for all strings. re-tuning as needed ( a lot) Sliding the bridge at an angle if needed.
Whats the action? That is how high are the strings (closer to the bridge vs nut)? If the notes are getting sharper the higher up the scale, sounds like there is excess string tension caused by the strings being too high closer to the bridge.
If this is the case, lower the bridge. I have seen this more towards the nut where the sharper bending form nut to fret causes the strings to add more tension, but yours is on the other end.
Else it it is intonation/scale like the others suggest.
I saw an old post the other day referring to Bill Nash's website www.nashguitars.com . This guy has a good list of tips and advice on how to tweak your guitar's performance and get it set up the way you want.