If in doubt, ask. Some tanks might not realise your healing ability, others might not have the confidence and are still learning or gaining that confidence or for whatever reason they're not able to handle big pulls. I've been levelling my PLD of late, if you had me in a party a few days ago if you felt my tanking was below par, it might have been but I had an injured arm, it was fine to play, but not at a higher capacity. And I know somebody who plays that has arthiritis, though she doesn't tank for that reason, but some might do so regardless. Some people have slower reaction speeds.
There's just a whole number of reasons to count that it just seems the best thing you can do when it doubt to just ask. I've had healers ask me to pull more and tanks ask if I'm okay with big pulls.
Just don't do what a tank did the other day and ask if it's okay and then pull everything before I could even finish typing a response, it makes the whole "asking" redundant.
But as somebody who has long been a healer main, I don't pull for the tank. I don't as a DPS unless I'm in the zone and forget myself...but that's because I'm being an idiot rather than trying to do their job for them. If I want tanks to respect me as a healer, then I in turn need to respect them as tanks. But I play all roles, so I know what might annoy me as a tank, healer or DPS and try to avoid doing those things.
And when tanking, if somebody pulls for me, I'll maybe give them a couple of chances, but if I am in on it with the other party members (as I sometimes queue with others) I might let them keep their aggro, I don't if it's going to ruin it for the rest of the party as not fair on them. But it's a practical method of showing why the tank tends to be the one who pulls. You don't know your tank's capability or confidence, hence they tend to control the pace, because it'll be a pace they (and hopefully the healer) can both handle.
But it happened to me the other day, I found both the healer and 1 of the DPS was having trouble in a dungeon, we wiped twice to the first boss, even after I explained mechanics. Fine, maybe it's a learning curve, not gonna hold anything against anybody.
Second boss, I figure, maybe I should stop and explain the mechanics to them to help them out, we stop for a moment so that I can do this, half way through typing them out the aforementioned DPS (who kept dying to the first boss) seemingly got bored and just pulled. Me, the healer and other DPS stayed on our side of the threshold and let him keep it. Sadly though, we learned the hard way here that it will now pull you in after a certain time, but DPS died and as were now drawn in, we just took over.
But ultimately, communication is key.