Learn Hardcore German: Mein Handgepäck ist zu schwer, deshalb lasse ich den Laptop zu Hause. - My carry-on is too heavy, so I leave the laptop at home.

Because Handgepäck is neuter: das Handgepäck.
In the nominative singular neuter (the subject form), the possessive mein- takes no ending:

mein Handgepäck (nominative, neuter, singular)

For comparison:

meine Tasche (feminine nominative)
meinen Koffer (masculine accusative)

Why does schwer have no ending in ist zu schwer?

Because schwer is a predicate adjective after sein (to be). Predicate adjectives in German don’t take adjective endings:

Mein Handgepäck ist zu schwer.

Adjective endings mainly appear when the adjective is in front of a noun:

ein schwerer Koffer
das schwere Gepäck

What does zu schwer mean грамmatically—how is zu used here?

zu + adjective means too + adjective (exceeding an acceptable limit):

zu schwer = too heavy

Don’t confuse it with:

sehr schwer = very heavy (strong degree, but not necessarily “too”)

Why is there a comma before deshalb?

Because this is effectively two main clauses joined in one sentence, and German typically separates such clauses with a comma:

Mein Handgepäck ist zu schwer, deshalb lasse ich den Laptop zu Hause.

You could also write it as two sentences:

Mein Handgepäck ist zu schwer. Deshalb lasse ich den Laptop zu Hause.

Why is the verb lasse placed before ich after deshalb?

Because deshalb is taking the first position in the clause, and in a German main clause the finite verb must be in position 2 (V2 rule). So the subject moves behind the verb:

Deshalb (position 1) lasse (position 2) ich …

This is normal “inversion” in German:

Heute gehe ich ins Kino.
Deshalb lasse ich den Laptop zu Hause.

Could I use weil instead of deshalb? What changes?

Yes, but the structure changes.

With deshalb, you have a main clause word order (verb in position 2):

Mein Handgepäck ist zu schwer, deshalb lasse ich den Laptop zu Hause.

With weil, you create a subordinate clause (verb goes to the end of the weil-clause):

Ich lasse den Laptop zu Hause, weil mein Handgepäck zu schwer ist.

Both are natural; they just package the reason/result differently.

Why is it den Laptop (and not der/dem Laptop)?

Because lassen (in this meaning: to leave something somewhere / not take it) takes a direct object in the accusative case.

Laptop is masculine: der Laptop.
Masculine accusative changes der → den:

der Laptop (nominative)
den Laptop (accusative)

What exactly does lassen mean here? Is it like leave or let?

Here lassen means to leave something somewhere / not take it along:

Ich lasse den Laptop zu Hause. = I’m leaving the laptop at home.

lassen can also mean to let / allow (a different common use):

Ich lasse ihn gehen. = I let him go.

So the verb is the same, but the meaning depends on the pattern:

etwas irgendwo lassen = leave something somewhere
jemanden/etwas
- infinitive lassen = let someone/something do something

Why is it written zu Hause with capitals? Is that a noun?

In zu Hause, Hause comes from the noun das Haus, and this fixed expression is traditionally capitalized:

zu Hause = at home

You will also often see the modern variant zuhause (especially in informal writing). Both are common, but zu Hause is the more traditional spelling.

Is Handgepäck always singular? How would I make it plural?

In everyday use, Handgepäck is often treated like an uncountable noun (like “luggage” in English), so singular is very common:

Mein Handgepäck ist zu schwer.

A plural die Handgepäcke exists but is less common and usually used when clearly talking about multiple separate items/pieces (e.g., in technical or administrative contexts). More natural alternatives are:

zwei Stück Handgepäck (two pieces of carry-on luggage)
zwei Handgepäckstücke (two carry-on items)