One option I haven't seen suggested here is to move the chord up the neck a bit instead of playing it with the open D. When playing any note, you are typically going to get a thicker sound if you play it on a thicker string. You can test this out by playing the open D string (just that note, for testing), then play the D on the 5th fret of the A string, then the 10th fret of the E string. You should notice that the tone gets thicker/warmer/more round. So if you were to play the D chord on the 5th fret, using the A barre chord shape, then you should find that your D sounds a bit fatter, potentially measuring up to the other lower root notes. The downside of this approach is that you will be changing up the voicing of the chord a little, where you will have a high A on top of the chord instead of the F# of the open voicing (or F if it's a minor chord). This would usually make the chord sound a little brighter, as the top note is a higher pitch, so it might not be appropriate for your sound. However, you could also just not play that high A and you would have the same notes as the open voicing.
Another option is to change up where you are plucking the string. When you pluck different parts of a string, you get a different tone. When you pluck near the bridge, you get a very thin sound, and when you pluck near or on top of the fretboard, you get a warmer/thicker sound. This is a little more difficult for beginners, since you have to pay more attention to your picking hand than you otherwise would, but it's good practice.
More generally speaking, it's good to consider the context. If you are going to be playing with a bass player, they will most likely be playing a nice fat root note under your chords, so the thickness of the root note on your instrument shouldn't matter too much when played in that context. It's also valuable to note that some frequencies carry better than others, so if you're playing this on an acoustic guitar, you're going to hear the frequencies a bit different than someone who is further away, so it could be good to set up a recording device across the room to hear it from the audience perspective and see if this is actually noticeable from there. You should also consider how important this really is. You may be paying a lot more attention to this tone issue than an actual listener would. So you might want to record yourself playing, then listen back and see if it really stands out while listening to the actual playing.