Why is this an issue? Spellweaver has one strong selling point - combat mechanics including speed which is unique and cannot be found elsewhere, which allows for indepth deck building strategies: a faster creature can outmanouver stronger yet slower creatures, compromizing strength minding your agility. However, in current state, there's almost no place for standard army building decks - near to every deck in ranked matchmaking is a heavy control lategame deck with one overpowered, broken combination that wins you a game after you ramp enough. This means near to zero diversity and not having to balance your deck according to different builds you encounter - you simply ramp and pull off your combo. Moreover, it discourages new players - they come, they try building a deck, they see these broken combos they can't keep up with without breaking the game themselves, they don't have the cards to do so, they quit.
I consider myself to be a card game veteran, I've played many of them and have seen multiple ways which game designers use for reducing the potency of cards for game-breaking intentions. I am quite new to this forum but I saw there are lots of active members in this community and a team aiming to balance it so I thought I could give my insights and, hopefully, help you guys fix this issue.
TL;DR:
Cards with passive abilities activated whenever X happens
There are cards with powerful abilities activated each time the condition occurs - the problem is that the condition is very ordinary and there is no cost for activating it. A great example would be Aezerthis, the Burning Agony.


I'm sure we've all seen it - they play a Voidtouched Subordinate, use Parallel Evolution to turn your creatures into a milling factory and then play Aezerthis which clears the board and damages you every, single, turn.
Such strong effects should not be possible to be activated multiple times, a simple "this effect can only occur once, during your turn" should solve it without making Aezerthis unplayable, it would keep her intended interaction, just would make it impossible to break the game with her.
Reanimating creatures you wouldn't be able to play without reanimating them
This is probably the most unfair thing among broken things: the fact you can play cards from your graveyard without meeting the requirements.


The strategy goes like this: you put a ton of overpowered creatures that require high levels, like Antriel, into a deck that doesn't even have shrines for playing them, but you don't care since you can reanimate without meeting any of these strict, high requirements. A simple solution would be to just add "you still have to meet the level requirements for the cards you wish to play" and it would be fair.
Legendary creatures are just common, run of the mill, overpowered creatures
There are many card games with "legendary" creatures - they have strong, unique effects, are generally stronger than what they should be considering their cost, but their amount is somewhat limited.


These legendaries are meant to be strong, extraordinary, but limited in quantity, unique. The fact you can only have one in play, but still four of them in your deck like any other creature is not enough to justify their straight up overpower value for cost. Card games are about controlling the board, a single creature is not meant to survive many turns (otherwise you've already lost anyways), so you aren't even expected to have multiple creatures of one kind on the board. A usual creature is played, does a thing or two and dies. The same goes for legendaries... which you can then summon again because you've got 4 copies of them - so much for being legendary and unique. A special mention goes to legendary creatures that have strong effects when played - you don't play them for their body, you play them for the effect, you don't care if you already have a copy in play because all you're concerened about is the effect they have when played - you can play Elinor when one is already on the board and not care about it being legendary because you just want the effect of recycling your spell.
Most card games have the concept of "legendary creatures" whose appearance is limited: it's usually limiting the amount of copies you have in your deck - 2 copies seems like a reasonable amount. Might & Magic, Duel of Champions (R.I.P. one of the best card games killed by its creators) had one of the best "legendary creature" limitation I've seen - you can only have 1 copy in your deck and when it's destroyed it is removed from the game entirely - it doesn't go to the graveyard, you cannot recycle or bounce it - it's gone, you'd better thought it over well before you played it.
This is also another thing that discourages new players - legendary cards are of high end rarity rating, and if they are just as common as normal creatures while being straight up more powerful it means this game is "pay to win" - therefore it is not noob friendly and paying for booster packs to get these rare legendary overpowered cards is the only way to go.
Strong active creature abilities without limitations for subsequent uses
The fact it's very easy to add energy on creatures makes spamming strong creature abilities is very unfair:


The idea behind creatures with energy is that you can use their abilities multiple times during one game, whenever you find it useful. However, if the ability is powerful there should be a limitation for using it multiple times in one turn, especially since it's very easy to add energy to creatures. A simple "subsequent uses of this ability in one turn costs you additional energy/mana each time" would solve it.
These are my general insights. I'm not trying to aim for specific card changes, just trying to highlight the general possibility of abusing certain types of cards in order to break the game. I hope it was of any use.