A heavier BB will carry it's energy longer, and is less susceptable to disruption. The result of using a heavier round will generally be an overall decrease in the distance your BB goes, but you well get an increase in the accurate distance.
What I mean is that a 0.20 may range 150ft, but you'll only have a reasonable degree of accuracy out to 80ft. A 0.28 will cut the total range down to maybe 120ft, but you'll be able to reliably hit stuff out to 100ft. Note that these numbers are arbitrary and I just chose them to illustrate my point/.
Having said that, your gun has to be able to put the energy behind a heavier shot. A stock TM gun performs worse overall on 0.28's than it does on 0.25's. As far as I'm concerned though if you're playing out doors and the gun is shooting 300 FPS or more, use 0.25 or heavier (I use 0.28 in all my guns).
Heavier rounds also penetrate brush a lot better and are less likely to be deflected by blades of grass.
"Someone in a Prius tried to race me at a stop sign the other day. I couldn't believe it. I had him for the first 100 feet or so but I can only walk so fast."