How can you tell when a lime is ripe for picking?

When they're green?

Here are a few links for you.

http://www.doityourself.com/stry/harvesting-citrus-lemons-and-limes

http://homeguides.sfgate.com/tell-limes-ripe-72820.html

https://www.gardeningknowhow.com/edible/fruits/lime/lime-tree-harvest-time-when-to-pick-a-lime-from-a-tree.htm

When I pick limes in the market, I look for ones with thin skins and heavy for their size.

Lucky you! I do great with the lemon, grapefruit and orange trees, but not so great with my lime tree. And I use limes a lot! Just think of all the stuff you can make with all those limes, homemade limeaid, lime pie, lime chicken, margaritas, virgin margaritas, lime sugar cookies . . . 😍

I test by pressing lightly on the sides. When I feel a little give it is ready to pick.

If your lime tree is as large as mine, you don't want to hand pick one by one. Also, the thorns are really mean! A commercial grower suggested I harvest the way they do. Spread one or more old sheets around the tree to catch the limes, then tap the trunk with a broom handle to gently shake the tree. Limes that are ripe will fall off the tree. Gather the sheets and sort (in the beginning you may have some overripe to deal with). This has the advantage of seldom having fruit on the ground to rot and attract vermin. Lime juice freezes wonderfully and you can make lots of friends since limes go with beer and are necessary for margaritas!!!

As far as heavy weight and thin skin, I found it was a matter of sufficient water for all my citrus. Yes, you can irrigate with your garden hose, but if you're a homeowner and can arrange to do so, run a drain hose from your clotheswasher to your trees. They don't mind the soap, bleach, softener, etc so why not get double use out of that precious commodity...water!