I can tell you from personal experience that the RF-62's will not be falling over any time soon, unless they are deliberately pushed over.
They weigh something like 57lbs each and they have 1 inch carpet spikes, they're difficult for a grown man to pick up and move, and although yes they in theory could be pushed over, again it would take deliberate effort, as in a toddler would have to be pushing his entire body weight horizontally and with great effort.
Also, i'm going to echo, the difference between the RF-52 and RF-62 is huge. The 62 has a different tweeter which makes literally ALL the difference.
As for the center, i've been told you can get away with an RC-52 instead of a 62, but i like to timber match my f/l/c so i splurged for the 62 /shrug.
To answer your last question, no, the rf-82s wouldnt be overkill, anymoreso than the 62's.
Edit: Also wanted to mention, the RF-42/52 use the same tweeter, with the difference being between the mid driver size. The 62/82 also use the same tweeter as each other (not the same as the 42/52), which is a much better tweeter than in the 42/52, but again the difference is in the mid driver's size.
Also, its very important that you provide sufficient and quality power. The Klipsch speakers have a high sensitivity rating, but that is mainly because the tweeters are horn loaded. It tends not to give the whole picture, as the mid bass drivers are nowhere near as sensitive as the tweeters. So what tends to happen is that when they're not given enough power, the tweeters play just fine, but the mid bass can't keep up, so the end result is the speakers sound excessively bright and harsh.
I reccomend at least 100watts continuous at 0.08%THD or better. And remember its also safe to go over on the power by a bit, so running a 200w/channel amp with the speakers when they're 150w rated will be just fine, as long as you're not trying to run things at 100% volume.
Edit: Also, almost forgot. You will absolutely want a decent sub. Regardless of what people say, short of $20k/pr floorstanders with true dedicated subwoofers built into them, the majority of floorstanders are incapable of producing robust bass. For example, the 62's are rated down to 38hz, but they do it anemically and with no authority. The moment i integrated a sub and crossed over the speakers at 60hz its opened the soundstage up and sounded absolutely fantastic.