A while back, I was under the belief that Tarble wasn't all that much of a weakling because he is still the blood of Saiyan royalty. People have said that Tarble is weak because he was sent away and unsuited for battle, however when you look back on Yo! Son Goku and Friends return (the manga especially), it was never mentioned that Tarble was weak since all Vegeta said was that he wasn't suited towards battle. His power was also high enough to be noted by people like Piccolo, Krillin, and everyone else immediately after.
That said, another thing that makes me further believe that Tarble wasn't weak at all has to do with the fact that in the broly movie, Raditz dismissed his little brother and labeled him pathetic for still being at home in a nursing capsule. Vegeta, on the other hand, merely wondered what happened to Tarble. If he looked at Tarble as weak, then he would have likely made a comment on it too (In all dubbed versions).
It's easy to say he was sent away so he's weak. And you can also point out that Tarble was influenced by those he grew up with which is why he was so soft, but if we're being honest, it has to be his personality as to why he was sent away. Special children like Prince Vegeta and Tarble and those other exceptionally gifted Saiyan kids shown in the Broly movie are put through a special regimen of training for the sole purpose of increasing their battle-power; if Tarble didn't have promise in the first place then he wouldn't have been put through training.
And I'm sure it's through his training where King Vegeta realized Tarble wasn't fit for battle because he's not the prideful, heartless, and sadistic Saiyan warrior that he likely used to be (and how Prince Vegeta turned out). Just looking at Tarble, he looks completely harmless. He gave Abo and Kado trouble by being fast and sharp enough to escape so he's definitely not incompetent or as weak as say, a Saibamen or even Freeza's best soldiers on Namek (maybe excluding Cui and those above).
Tarble also had to be just a couple to a few years younger than Vegeta to make the timeline match up. If he was automatically looked at as weak, he would have probably been sent away even longer ago assuming King Vegeta wouldn't have a tolerance for weaklings in his lineage.
I'm not saying that Tarble is stronger than his brother naturally, but still strong. King Vegeta probably hoped having another son meant he'd have another child to shatter power-level records or have similar growth to his first born.
I stand by Tarble having great latent potential and still being strong, but also failing to capitalize on it because he doesn't like to fight, so he doesn't spend his time training and sharpening his Martial Arts/Combat skills.
In a way, he's like the opposite of Gine. She was a low-class warrior who was strong enough to become a combatant, but her kind nature in combination with her weak power caused for her to be pulled off the combat squad. Tarble, on the other hand, is a strong Saiyan with great upside potential of being a great warrior, but is too kind-hearted and doesn't have the drive to fight - and in his case, kill innocent people. We see that there are countless normal Saiyan workers who couldn't care less about destroying or fighting and the majority of Saiyans are particularly weak (in our common standards these days) in their base forms alone. Tarble was probably one who was fairly strong but King Vegeta expected far more than just greater power. He wanted another prince who would also meet the same characteristics of a potential king, as he was meant to be a continuity of his bloodline and extra insurance for his blood having the right to the throne (and for eventually warring with Freeza, I'm sure).
Had he realized that Training was a thing capable of increasing his son's strength, he would have maybe been more inclined to keep him around. Tarble was taught how to use a scouter, read, math, and all of the other basic stuff...King Vegeta was realistically smart and sound but logically, he was dumb as hell.
Look, Tarble is NOT some super elite warrior freak with a power-level of 100,000+ in his first introduction because he is not a battle-hungry Saiyan and that also implies that he doesn't train very much. What I am saying though is that he has to be powerful by Saiyan Saga standards. I'd have him no weaker than Goku's suppressed power-level of 5,000 when he first showed up and nothing higher than 40,000. It's a large gap in-between, but still a relatively powerful energy to feel coming into Earth out of nowhere.