Here is another view point.......... I have a 53 x 39 double chain set, I live near the Pennines, but don't need more than 39 x 21....
Point is, we all have different needs..... if you think a compact might help, then get one, but look at a gear calculator (just google it) and it will give you an idea of what you might need.... - i.e. if really struggling on what you have, see what a compact gives you..?
How do you know you have a heavy chain set...? That doesn't help climbing...... Body weight and fitness.... that's it.... chain set...oh maybe 1 second or two...drop a load of flab...or get fit.......oh.... minutes........
PS I run top end stuff and mid range stuff. The top end is better as the 'whole package' is better..... can't really say how much an improvement a single part might make...
Do not get sucked in by marketing rubbish.........