To "play over the changes" first forget playing over "chords". The changes that are happening are KEY changes, not CHORD changes.
Arpeggio's are one thing, but chord functions and how to treat them are where a lot of the "jazz sound" comes from. Sure you have the chords in front of you and you can follow them with arps or scales, that's the "one-dimensional" approach. It's very usable, but after one or two passes, it'll be obvious you don't have too much more to say than you already did.
Things turn into jazz when you understand a few other dimensions...chord functions, chord substitutes, chromatics, swinging the beat, etc...
To play over changes you first need to pick out Keys, what chords belong to what Key. And, when the Key changes, what's the chords function is in the Key. You are not necessarily playing over "chord changes" but "Key changes" and the functions of the chords within the Key.
If you stayed in one Key throughout a whole song...there's no "changes" going on. You would be in one Key, all the chords relate to the each other Diatonically using the same notes. The only way to get a "jazz sound" here is to look at chord functions...but again, no REAL Changes going on.
But, as soon as that Key changes...if you remain in the old Key it usually isn't going to sound very good, so you HAVE TO change Keys. And you need to look at the chords of this new Key and their functions.
Now there are VERY COMMON progressions found in almost every tune (especially Jazz standards) that you find all over the place...the ii-V-I, the vi-ii-V-I, I-IV-V, iii-ii-I.
Funny things is once you get into it, with functions and subs, you'll see they all do pretty much the same thing...they find a smooth transition BACK TO THE I CHORD. And a lot of times they can be played over using the same concepts.
Most of the time they "cycle back through the Circle of 5th's". They use "cadences", (if you're not aware of both the Circle and cadences, I will show them but, get on the Internet and look up more info on them, they explain a lot) Look at the Circle of 5th's...

Pick the Key of C Major (right at the top)...
If you want to play a ii-V-I move three steps clock wise from C on the circle...you land on D, make that a minor chord, so Dm...from D move one step counter clockwise to G, make that a major chord, so G...now move one step counter clockwise from G, moving "Back to" C.
So a ii-V-I in the Key of C Major is, Dm-G-C.
So a ii-V-I uses three chord in succession back pedaling up the Circle of 5th's "back to" the I chord.
Ok, now look at the vi-ii-V-I progression...we'll stay in C...and start with C on the Circle...
Move up 4 notes clock wise from C...to A, make that a minor chord, Am. Now move back one from A to D and make it a Dm, now move back one more the G and make it a G Major chord, and then one more to C and make it C Major.
Now you have Am-Dm-G-C, which is a vi-ii-V-I in C Major.
Using the Circle you can start ANY WHERE, work your way back through the Circle making each group of 3 notes a ii-V-I and you'll cycle through "CHANGES".
One thing that makes all of this even stronger is, make the ii chord a m7, the V chord 7 (dominant chord) and the I chord a maj7...so in the Key of C you'd have Dm7-G7-Cmaj7. This will help you state the Key stronger.
Check this, starting to the left of C...on the F note...
||: Fm | Bb7 | Ebmaj7 | Ebmaj7 | Abm7 | Db7 | F#maj7 | F#maj7 | Bm7 | E7 | Amaj7 | Amaj7 | Dm7 | G7 | Cmaj7| Cmaj7 :||
Notice how every three chords (every four bars) the Key changes, and each little ii-V-I keep moving itself back to the Imaj7 of it own Key. There are MANY ways to connect these, and they all sound pretty much right, and usable.
I'm not sure if that example is a real jazz tune on not, but I know for certain it was/is a way people practiced "PLAYING THROUGH CHANGES"...again, not CHORD changes, but KEY changes.
Now try this with the example above, when you finish all the way through to the last Cmaj7, jump to the note just left of the F you would originally have repeated...and then continue through more ii-V-I's...so after Cmaj7 go to Bbm7-Eb7-Abmaj7...then keep moving back through the Circle in the same manner...like so...
||: Fm | Bb7 | Ebmaj7 | Ebmaj7 | Abm7 | Db7 | F#maj7 | F#maj7 | Bm7 | E7 | Amaj7 | Amaj7 | Dm7 | G7 | Cmaj7| Cmaj7 | Bbm7 | Eb7 | Abmaj7 | Abmaj7 | Dbm7 | F#7 | Bmaj7 | Bmaj7 | Em7 | A7 | Dmaj7 | Dmaj7 :||
You can tie this of at the end with Dm7-G7-Cmaj7 like so...
|| Fm | Bb7 | Ebmaj7 | Ebmaj7 | Abm7 | Db7 | F#maj7 | F#maj7 | Bm7 | E7 | Amaj7 | Amaj7 | Dm7 | G7 | Cmaj7| Cmaj7 | Bbm7 | Eb7 | Abmaj7 | Abmaj7 | Dbm7 | F#7 | Bmaj7 | Bmaj7 | Em7 | A7 | Dmaj7 | Dmaj7 | Dm7 | G7 | Cmaj7 | Cmaj7 ||
NOW, try it all starting anywhere and using a vi-ii-V-I progression, still just back pedaling through the Circle of 5th.
A I-IV-V is looking at the Tonic, let's stick with C as I, the IV is F which is one note to the left of C on the Circle and then the V, G, is one note to the right of C on the Circle...
So, guitar wise, and pitch wise, when playing ||: C | F | G | C :|| (pretty much King Of the Road)...it seems like you move UP from C to F, then UP from F to G, then DOWN from G to C...but "Circle wise" you are move DOWN from C to F, then DOWN from F to G, then DOWN from G to C...DOWN also means BACK, so you are again "back pedaling" or back cycling through the Circle of 5th's.
Now here's you task as you try to tackle "PLAY THE CHANGES"...
Go back to the ii-V-I examples and figure out what Major Key each of the ii-V-I's is from, start by playing the Major scale of the Key over it's chords, then when you next set of chords comes up, CHANGE KEYS to the new Major scale.
This is the BEGINNING of PLAY OVER THE CHANGES.
The next step to having it sound like Jazz is to learn how to treat the "function" of each chord in the Key. This will allow you progressively ENHANCE the sound of everything MOVING BACK TO THE I CHORD.
After that there are plenty of others things that can help you play over the changes even more deeply...but these are the basic fundamentals to get down first...recognition and understandi
