The peg is probably loose because the string is smaller and not taking up as much room in the hole. You have made the peg holes bigger by using the big strings, take the big strings away...
The bigger the string, the slower it wants to vibrate. The smaller the string is the faster it wants to vibrate. In order to tune a big string and a small string to the same pitch, the big string will need more tension on it than the small string.
Think about it, if you try to tune your low E string to a G, do you add tension? If you tune your A string to the same G, don't you loosen it? Tune both strings to a G, I'll bet the heavier string has more tension on it.
Your issue is with your bridge pegs, not a problem with too much string tension.