Sounds like he's a smart cat and knows that wet food is better for him than dry.
How much of the dry does he eat over the day, do you know? You can figure this out by weighing the dry food bowl before and after you fill it and keeping a log for a couple of days of how much disappears per day on average. Then you can figure out what proportion of the recommended feeding amount for his weight that is.
If you're feeding him 1/4 can in the morning and 1/4 can in the evening, that amounts to a third of the recommended daily amount for him (which would be one and a half cans if only fed canned). He should be perfectly fine as long as he doesn't eat more than two thirds of the recommended amount of the dry in addition to that (e.g. if the recommended amount is a cup, he should not be eating more than 2/3 of a cup). If you're concerned about him gaining weight because he eats too much, you can put just the appropriate amount of dry food into his bowl each day. Of course that might result in even more begging for food! If he doesn't even eat the recommended amount of the dry food, he might simply not like it and prefer to go hungry and bug you for wet food instead. No harm in giving him more of the wet in that case - it's mostly water anyway, so unless he eats a lot of dry food with it it's unlikely he'll gain too much.
If he's eating in total a lot more than he used to or should be eating, I would also talk to the vet about it. It could be an overactive thyroid or something else going on. I've had fosters who were exceptionally ravenous and it turned out they had tapeworms. Better to get any medical issues ruled out before assuming it's a behavioral thing, especially if he's already older. Sometimes older cats don't digest food as well as younger cats and have a harder time extracting the nutrients from it, so if that's the case he might really still feel hungry even though he's eaten the recommended amount.