Keep playing your DRK and you will get more insight into what's going on with tanks while they're tanking. I bring this up first and foremost so you can eliminate any doubt on your part if you are the problem, as you will be able to gauge how much experience your tank has tanking. There is also no shame in telling your tank to ease up a bit if they are taking too much damage. If they decide to be jerks about it, you can leave any group that makes you uncomfortable.

There can be a lot of reasons for a tank being squishy. Bad/broken gear, over-confident and tries to take on large pulls out of tank stance, has no idea mitigative CDs exist or doesn't know how to rotate them properly, stands in AoE. The list goes on. What it always comes down to is they are simply taking on more than they should, which might even be the dungeon he/she is in with you. If the tank's HP drops too quickly, and the mobs are dying slowly, the pull is too strong for your group.

The issue is you keep getting inexperienced tanks, and likely a mix of low DPS due to under-geared DPS players and also no DPS contributions on your part because of the need for constant healing. An experienced tank will gauge the strength of the party. Some are more careful and will do a small pull first. Others are reckless and will pull everything at the start and simply see how everyone does and adjust accordingly. This tank usually checks everyone's gear prior to doing so, so he's not totally reckless

As you say, sometimes we get the ones who can pull huge while giving us ample windows to DPS, others require much more intensive healing on our part. I do sympathize with you, but it is also something that us healers have to adjust to. It is a lot of fun to weave in DPS skills, but we're healers first. Always.