Ahh, FUN WITH ROCKS!! Depends. What kind of rocks. Lava rock is lighter than most others. Artificial is even lighter

How big a pile do you want? Over how much space? How big, and what shape are these rocks? Of course you can have more smaller rocks. Caves = less weight.
What kind of tank do you have? Standard, ALL-GLASS AQUARIUM 55 Gal has a tempered bottom. Standard, Perfecto/Marineland 55 Gal has all tempered glass. Tempered glass is stronger. Best figures I can find say that should withstand @8,000 PSI(pounds per square inch of pressure) so theoretically you could have as much as you want.
Disclaimer- I have never attempted this so don't personally know it to be true.

Also, have no experience with acrylic tanks.
My flying guess is 20 to 30 lbs? for one side of the tank.
Make sure the stand and tank are plumb and level and the floor can handle the load.
You want to distribute the weight as evenly as you can over as much space as possible to reduce pressure points.
To do this place a piece of eggcrate(plastic light diffuser grid- found at Home Depot, lowes, etc.) On the bottom glass of the tank. Make sure it's flat on the glass, not on the silicone or anything else. Place your rocks on this, biggest towards outward edges
and on the bottom. Then you can fill in around the bottoms of the rocks with substrate to hide the eggcrate.
Eggcrate also prevents fish from digging under the rocks.
I have found it helpful to make a template of the tank bottom out of cardboard or newspaper. Lay this on a sturdy table, place your piece of (cut to size) eggcrate and practice stacking your rocks on it first.
Much easier than trying to maneuver in the tank.
Some things to keep in mind -
Looking at lots of pictures of other aquariums and rock formations in nature can help you decide what you want to aim for. And make you start twitching for more tanks!
It's fun and a lot less expensive to poke around the landscaper's yard to find your rocks. You might want to bring some buckets, milkcrates, or whatever to carry your rocks.
Extra muscle is always appreciated!
Clean your rocks - brush well with 1:19 bleach/water then rinse well with clean water with dechlorinater added and let dry
'Flat' stacks easier than 'round'
Using the same kind of rock or similar usually looks better than mixing a bunch of different ones
Keep your plane of orientation fairly consistent, that is, striations, lines, cracks, surfaces should be placed to run in the same direction
Aim for stability and/or stick 'em together with tank-safe silicone, epoxy, or cyanoacrylate(crazy glue gel is used for corals also)
Experiment - flip, turn, move those rocks around. Some have prettier faces than others, some play nicer with others, some just can't fit in.
As you do, you'll notice that ,like a jigsaw puzzle, they fit best in certain ways(not always the way you think they should go)
Takashi Amano says "don't use a rock in a way that contradicts it's essence"
Stare at them for a while and it starts to make sense!
Keep the overall composition of the tank design in mind and frequently take a few steps back to make sure you like the way it develops.
As far as the balance question, you can also add plants to the rocks if it looks too bare. Some suggestions - Mosses(java, willow etc.), african or java ferns, and anubias can all be easily attached to rocks. Much easier to attach before you put them in the tank!!!
Take your time, have fun, and POST PICS PLEASE!!
ROCK ON!!!