Thanks everyone for the responses. I think that is what he is doing. It is funny I suppose you could rule a larger creature trying to grapple a smaller one using Dex to evade should have disadvantage (or give advantage to the smaller dodger). How many times have we seen or read about small heroes evading large ogres or giants trying to grab them?
I think it makes since if the creature being grappled is larger and resisting with Str, especially if it is 4-legged. But I'll talk to him next session and the rest of the group. Our DM pretty much goes with the consensus of the table unless he feels really strongly about something.
I personally find the difficulty catching something half your size being difficult because of dexterity to be very bad writing. If your trying to catch something like a mouse or fly that is supper fast and small its fine but as an adult catching my nieces and nephews my 3ft arm reach means I pretty much catch them before then can run and I can tie them up in my long arms an tickle torcher them pretty much with out fail. Its easy to explain the use of bad rule with bad writing but that doesn't make the rule or the writing better. Its kind of like, well all villains with guns that could one shot heroes are required to throw there gun down a pull a knife instead of just shooting the hero in the head... "because its personal" but later when the hero manages to get the gun he does not hesitate to show the villain between the eyes... I am sure we have all seen that in book and movies more than a few times too but that doesn't mean in D&D I will ever have a villain discard his advantage.
Players: "we sneak in the bosses thrown room after blowing up his guards our side with fire ball"
GM: "sure roll for stealth then roll for perception"
Players: "Got a 10 for stealth and a 15 for perception... why are we rolling for perception?"
GM: "the boss heard the fire ball and hide too, you didn't see him but he did see you... which is unfortunate because he now stabbing your cleric with large marked shield flaunting that he is healer in the back, roll initiative"
Players: "What what?!?! he wasn't sitting stoic waiting to villain dialogue and us to get a free ambush like all the movies!?!"
GM: "No he figures you killed all the guards on the way to him so your not really in a talking mood and you survived it so he is not taking you lightly. He instead is thinking he should kill any healers he can guess as quickly as possible to increase his odds of survival"
. . . I see no reason to follow bad tropes in D&D. If your Gnome has haste I might give have advantage for being fast but his dexterity (acrobatics) is his skill level on avoiding being grappled. They don't necessarily have any more agility.
You can be small, slow, and unagile. You can also be large, fast, and nimble. Those traits might be considered more come in one or the other but your character design determines if its actually true for your character. Like I said, that goes both ways... I would not get a creature advantage on grappling for being one size larger since its not inherent that being large makes you proficient at grappling things you could simple be uncoordinated. I might make slick floors, low ceiling, or if its a monster extra long arms like a Giant Ape, I might give it advantage.