Me and a friend are creating barbarian brother characters. I know Goliaths are no longer an option, but are we able to make our characters a bit taller and heavier than the restrictions set in the player's handbook? Like, could we make 8ft tall, 300lb barbarian brothers?
Goliaths are Normal
If you want to make Goliaths, you can do so for free. See the first link.
If you want more, see the second link. It costs money, so if you don't want to have to buy a supplement, that's understandable. This race seems to fit what you are looking for:
Size. Goliaths are between 7 and 8 feet tall and weigh between 280 and 340 pounds. Your size is Medium.
Ability Score Increase. Your Strength score increases by 2, and your Constitution score increases by 1.
Natural Athlete. You have proficiency in the Athletics skill.
If you are interested in home brew, all you need is the DMG and your imagination. If your desire is to build big barbarians, nothing is stopping you. The key thing to recall when trying out your own creations is that all of the character races are "medium" in size (save gnomes and halflings). Making a PC size "large" moves some of the balance points around, for example damage dice may change.
DMG pages 285-288 covers making new player races.
Note on Adventurer's League character creation: the general rule is "PHB +1" (one other supplement, be it Sword Coast Adventures Guide, Volo's Guide, or one of the other supplements like the Elemental Evil Supplement at the link). You need to work with the GM to ensure that the +1 fits within Adventure League guidelines. (Link is to the AL Player's Guide for the Storm King's Thunder season).
(AL P. G. pages 2-3) You may use all options presented in the Player’s Handbook with regard to race and class, in order to build and advance your character. For example, if you are playing a human, you are allowed to use the Variant Human Traits, as presented on page 31 of the Player’s Handbook. In addition to the Player’s Handbook however, you may also choose to use one other resource from those listed below to build your character.
• Elemental Evil Player’s Companion
• Sword Coast Adventurer’s Guide
• Volo’s Guide to Monsters
There are no explicit height and weight restrictions for humans (or other races)
While the text on humans lists typical sizes, and the rulebook offers a method of determining size randomly within certain limits, those are listed as guidelines or tools, not explicit restrictions. As such, you can - as long as your GM approves - set your height and weight freely.
The rules on size category are similarly abstract - a human is size category medium, regardless of its actual height and weight. While the size category "medium" is described as "roughly between 4 and 8 feet tall", that is again stated as a rough guideline (and your barbarian would still fit within that range).
As always, your GM might put limitations on your character if he feels that it is sufficiently outside the norm that it doesn't fit in his campaign, which the physical size of races would certainly fall under. As your character would be unrealistically large, it would be a good idea to bring this up in advance.
All the above applies to your listed height and weight, which have no effects on the game rules (apart from how difficult you would be to carry). Your character should likely to have above average strength and constitution, but those are determined as normally by the rules.
If you wish to also gain the mechanical effects of being larger, you would have to either adopt a house rule or use the Goliath (or another) race, as described in other answers.
I agree with Korvin, you can use the Goliath supplemental material. If you make a "human" who is 8ft tall, you would need your DM's permission, and then homebrew rules similar to the following:
Apply the size "large" modifiers, which include occupying 4 squares or 3 hexes, use of large weapons, increase in price of equipment (especially clothing), and your 6 stat points for "human" would probably either be rewritten and reduce to Str +2, Con +1, or more likely, Str +1, Con +1, and you have a special feat: Large.
Your DM may also say you have a base speed of 35 instead of 30, in addition to applying several "large" penalties, like being easier to hit, being surrounded by more targets, etc.
As a standard ruling, no, you cannot play 8ft tall humans and get the size modifiers.
As a home brew, you can do the above.
As a legalistic approach, you can either create a Goliath, or take a human with a high strength and constitution, a lower dexterity, and then take equipment and feats approximating some aspect of being large, such as use of large heavy weapons, and any of the following feats:
- Durable (+1 Con, min hp/hd)
- Grappler (creatures one size larger don't automatically win)
- Great Weapon Master (very good with enormous weapons)
- Mobile (flavor text it so instead of being agile, you are just so tall your speed increases and difficult terrain is just too small to bother you)
- Tavern Brawler (your huge fists do 1d4 lethal, +! str or con, and you are good at grappling puny men)
- Tough (a man of your size has 2 more hp/level than smaller folk)
Then all you have to do is stick with Barbarian to 20th level, try to get a 20 strength before then, and your +4 to con and Str will give you a 24 strength, which is better than a frost giant and much better than a hill giant. Additionally, if a Wizard casts Enlarge Person on you, your grappling feat allows you to grapple Huge creatures (i.e., things like Hill Giants)